Primal infeasible. This last term refers to a technique that allows some of the best solvers out there (e. In such a case MOSEK returns a certificate indicating primal or dual infeasibility. This is the Aug 25, 2025 · 8. mps files with those different solvers? Because if that is the case, the problem now is actually with the lpsolve package in R. That is, instead of saying that a tableau (or dictionary) is feasible or infeasible in the usual sense, we will now say that the tableau is primal feasible, respectively, primal infeasible. We would like to raise some dual variables, thereby increasing the dual objective, until some dual constraint goes tight, at which time the primal complementary slackness conditions would indicate that it Jun 3, 2020 · Either the Primal and Dual are infeasible or the optimal value is 0. Condition (10) of Farkas' Lemma0 does not hold, so (20) must hold, i. How and 6. Primal feasible and bounded, dual infeasible is impossible: If the primal has an optimal solution, the duality theorem tells us that the dual has an optimal solution as well. For each , y is dual-feasible since AT y = and y = y + ^y 0: The objective value of y is Aug 25, 2025 · 7. Lecture 15 Primal-dual interior-point method primal-dual central path equations infeasible primal-dual method Finally, note that ProxQP has a specific feature for handling primal infeasibility. Aug 17, 2015 · ECOS incorrectly determines the problem to be infeasible, which is weird, since it just solved the minimization version of the problem without any trouble. Dual variables are related to the Lagrange multipliers of the primal constraints. unknown — the solver was unable to reach a conclusion, most likely due to numerical issues. Aug 25, 2025 · 6. res. Oct 2, 2009 · This is equivalent to setting pi to zero. Dec 8, 2018 · If the primal is feasible and bounded, then the dual must also be feasible and bounded and they must have the same optimal objective value (this follows from strong duality for linear programming). Path-following primal-dual interior-point methods generate search directions from perturbations of the KKT system F0, and choose step lengths k with reference to central path neighborhoods. Aug 25, 2025 · primal/dual infeasible — the problem is infeasible or unbounded or a combination of those. Similarly, when the dual linear program is infeasible, the primal linear program has an unbounded ray. In this lecture, we will look at another approach to LP relaxations, in which we will construct a feasible integral solution to the LP from scratch, using a Dec 17, 1996 · The major primal-dual algorithms covered in this book are path-following algorithms (short- and long-step, predictor-corrector), potential-reduction algorithms, and infeasible-interior-point algorithms. For example, the constraint $2x = 1$ is actually implemented as $|2x - 1| \le \varepsilon$, where $\varepsilon$ is a small solver-dependent primal feasibility tolerance that is typically on the order of 1e-8. Since the original primal problem had an optimal solution, so did the original dual problem (strong duality). 1], if the problem is primal infeasible, then y = limk!1 yk satis es conditions (12), whereas x = limk!1 xk satis es conditions (13) if it is dual infeasible. A feasible primal solution—if one exists—can be obtained by setting ObjectiveSense to FEASIBILITY_SENSE before optimizing. there exists ^y such that AT ^ = 0, ^yT b < 0, and ^y 0. , in dynamic problems where constraints change). The dual of a given linear program (LP) is another LP that is derived from the original (the primal) LP in the following schematic way: Each variable in the primal LP becomes a constraint in the dual LP; Each constraint in the primal LP becomes a variable in the dual LP; The objective direction is inversed – maximum in the primal becomes minimum in the dual and vice versa. (= Weak Duality Theorem Primal infeasible, dual infeasible (in nite gap). Feb 3, 2024 · But solvers can return infeasible points, nearly feasible points, or certificates, so returning a value does not mean that the value is good. prim_and_dual_feas. Also, when I set the objective function to a constant and then solve the problem, it turns out to be optimal. When the dual is infeasible, the primal is unbounded if there exists a feasible primal solution. March 27, 2006 Abstract Primal–dual interior point methods and the HKM method in particu- have been implemented in a number of software p amming. I recommend Google searches for infeasible interior-point methods, symmetric primal dual methods, and homogeneous self-dual embedding. workspace ()来检查OSQP内部状态。使用osqp求解QP问题时，无无 Our primal-dual algorithm starts with the primal infeasible solution x = (0; : : : ; 0)T and the dual feasible solution y = (0; : : : ; 0)T . Since the primal is unbounded, there exists an ^x such that c^x < bT y, contradicting the Weak Duality Theorem Nov 28, 2018 · I'm trying to solve a QP problem by using osqp-matlab but seems the solver is not able to find a feasible solution. 25. Since it is not known beforehand whether problem (13. Feb 25, 2020 · 问题与解决状态： 问题状态：feasible；primal/dual infeasible; unknown 解决状态：optimal；certificate（不可证明）；unknow（不可解） 典型的报告状态： 检索解决方案值： Model. Therefore, most solvers stop after they prove the dual is infeasible via a certificate of dual infeasibility, but before they have found a feasible primal solution. the primal is infeasible. 5 days ago · Primal-dual infeasible interior-point framework is a class of algorithms that solves convex optimization problems by enforcing feasibility progressively through penalty functions and barrier regularization. dualObjValue — the primal and dual objective value Variable. 1 Dual of quadratic program Consider a quadratic program with Q 0 Chapter 8 Weak and Strong Duality We’ll now prove several theorems relating the optimal objective values of the primal-dual pairs. This theorem for ows Nov 21, 2017 · In addition, our technique is the first operator splitting method for quadratic programs able to reliably detect primal and dual infeasible problems from the algorithm iterates. The minimum of this and dual_feasibility_tolerance is used for the feasibility tolerance of ‘highs-ipm’. 2 We can in fact easily show that if either the primal or the dual has a finite optimum then so does the other. 22 Consider the dual simplex method applied to a standard form problem with linearly independent rows. The relation between an LP and its dual is extremely important for understanding the linear programming (and non-linear programming, indeed). Primal infeasibility is certified by a vector v that satisfies A T v = 0, u T v + + l T v − < 0. On the primal dictionary: w2 leaves, x2 enters. Supply, demand and cost of transportation per unit are given in Fig As in many primal—dual interior-point algorithms, a primal—dual infeasible-interior-point algorithm chooses a new point along the Newton direction towards a point on the central trajectory, but it does not confine the iterates within the feasible region. I can see while my model runs that in case of infe Infeasible Primal-Dual (Path-Following) Interior-Point Methods for Semidefinite Programming* Yin Zhang Dept of CAAM, Rice University Sep 8, 2025 · In addition, our technique is the first operator splitting method for quadratic programs able to reliably detect primal and dual infeasible problems from the algorithm iterates. Feb 11, 2024 · When using the CPG solver from the cvxpygen project on a valid optimization problem, the solver reports a 'primal infeasible' solution, while the conventional solver produces an optimal solution. May 12, 2016 · By the strong duality theorem we know that LP can have 4 possible outcomes: dual and primal are both feasible, dual is unbounded and primal is infeasible, dual is infeasible and primal is unbounded It is not always possible to find IIS isolations. 11. Solution status Introduction The primal dual algorithm, while not a good general purpose LP solution technique, is valuable because it is easy to customize for a particular problem. Similarly, if the dual is unbounded, this immediately implies that the primal must be infeasible. By construction, I know a feasible solution exists. Oct 5, 2021 · Try lowering the primal infeasibility tolerance to something like 1e-6 or smaller and see if it returns a feasible solution them. But it's possible for both the dual and the primal to be infeasible. What can be the r Status values and errors Status values These are the exit statuses, their respective constants and values returned by the solver as defined in constants. We discuss this approach in Sec. At the final (optimal) solution, the basis is both primal and dual feasible. mini As for the (Infeasible, Infeasible) entry, it is quite easy to see it is possible: suppose the primal is infeasible, then we write its dual and add more constraints to make it infeasible, and the primal obtained from the new infeasible dual still is infeasible. sol. 8) is infeasible (has no feasible solution), MOSEK will report a certificate of primal infeasibility: The dual solution reported is the certificate of infeasibility, and the primal solution is undefined. Dual simplex is exactly analogous to primal simplex where we start with a dual feasible solution corresponding to a basis B and move towards deduct that strong duality holds if it is feasible. 8. However, if the primal is infeasible and the dual is feasible, then the dual must be unbounded. There seems to be a problem with the canonicalization. See example below ln ) iterations, where ν is the parameter of a self-concordant barrier for the cone, ε is a relative accuracy and ρf is a feasibility measure. p⋆ is the primal optimal value; d⋆ is the dual optimal value p⋆ = +∞ if primal problem is infeasible; d⋆ = −∞ if dual is infeasible p⋆ = −∞ if primal problem is unbounded; d⋆ = ∞ if dual is unbounded Oct 20, 2022 · With regards to linear optimization using the simplex method, can someone provide an example: where both the primal and dual of problem A are infeasible where both the primal and dual of problem B MOSEK determines if either the primal or the dual problem is infeasible by means of a Farkas certificate. This theorem gave us a method to prove that a given ow is optimal; simply exhibit a cut with the same value. A convergence proof is included. 6 days ago · Infeasibility Analysis # You have a few options if a model is found to be infeasible. However, it was solvable with another solver as well as with less data. There are also messages available at log level 2 (the most likely useful relate to scaling), and will be addressed in a future version of this User Guide. This is the Jun 3, 2019 · However, if I try to update Ax, q, l, and u (my P matrix stays the same), I get a report of primal infeasibility each time. 681476 323874 piecewise_jerk_path_optimizer. Mar 26, 2024 · I came across your library and have been trying to apply a simple convex combination problem to it but I keep getting primal infeasibility when adding the boundary constraints for the problem. Consider the family f solutions y = y + ^y, 0. Suppose that we have a basis which is primal infeasible, but dual feasible, and let i be such that xB (i) < 0. 0 scipy 1. primal/dual infeasible — the problem is infeasible or unbounded or a combination of those. Jun 23, 2023 · Using matrix inversion we can easily find a solution which satisfies all the constraints, but OSQP with its conditions can not find this solution and gives primal infeasible. When one is infeasible we can say that the other is either unbounded or infeasible. Note that most infeasible models are so due to bugs which can (and should) be more reliably fixed manually, using the knowledge of the model structure. of that problem is infeasible. It decouples primal and dual updates via operator splitting and proximal mappings, enabling flexible handling of infeasible starting points. 12. Apply your subject matter knowledge of the problem you are solving. In this case, the primal cost is −∞. 6 Retrieving infeasibility certificates ¶ When a continuous problem is declared as primal or dual infeasible, MOSEK provides a Farkas-type infeasibility certificate. Furthermore, both problems seems to be optimal when I use KNITRO. Recall that the regular (primal) simplex method is an algorithm that maintains primal feasibility and works towards dual feasibility. As mentioned previously, these theorems generalize to non-linear programming and are important for analyzing the solution spaces for both linear and non-linear programs. Several papers are available on the internet where Duality theorems are discussed. Solution status Sep 15, 2019 · The primal infeasible means the optimizer proved that it's impossible to find a solution for that problem. Surprisingly, I have seen that one of the binary variables in the solution ha. Even if there is a FEASIBLE_POINT returned, it does not mean that the point is optimal. itr. Feb 3, 2020 · Cbc tells me that my problem is infeasible. Aug 25, 2025 · 8. Aug 25, 2025 · This is in fact what happens inside MOSEK; for efficiency reasons MOSEK converts the problem to standard form before solving, then converts it back to the input form when reporting the solution. Some theorems related to dual and primal problems are stated and explained. Our algorithm is very robust, placing no requirements on the problem data such as positive definiteness If the problem is primal infeasible, then y := limk!1 yk will satisfy conditions (12), whereas x := limk!1 xk will satisfy conditions (13) if it is dual infeasible. As described, the primal simplex method works with primal feasible, but dual infeasible (nonoptimal) bases. , pinks on the left, not on top). OSQP solves convex quadratic programs using an ADMM algorithm and can detect primal infeasibility. Showing both primal and dual dictionaries: Looking at dual dictionary: y2 enters, z2 leaves. h. Diagnosing Infeasibility # It just works! Detects primal / dual infeasible problems When the problem is primal or dual infeasible, OSQP detects it. However at some point the global upper bound was updated (and made finite) in spite of the LP relaxation's infeasibility. Please also refer to our examples on coping with infeasibility. Debugging infeasible models - YALMIP Nov 2, 2020 · E0227 18:00:43. slx and so on — dual values for the Aug 25, 2025 · 6. Once you have improved that, if the problem is still reported infeasible, carry out the guidance in. Feb 16, 2023 · It appears Mosek was provided the dual by CVXPY. 13 Retrieving infeasibility certificates ¶ When a continuous problem is declared as primal or dual infeasible, MOSEK provides a Farkas-type infeasibility certificate. The dual simplex method adjusts the dual solution efficiently to A return status of DUAL_INFEASIBLE does not guarantee that the primal is unbounded. Because there can be a case when both are infeasible. pobjval, res. For example, when the primal problem is infeasible, the dual could be either unbounded above or infeasible. So Mosek's declaration of dual infeasible corresponds to primal infeasible of original problem (as stated in Summary, apparently produced by CVXPY, which states infeasible). X; Z 0 Infeasible Alg: allows infeasible iterates Primal-dual Alg: perturbed and damped New-ton (or composite Newton) method applied to a form of optimality condition system. After an optimal but infeasible first phase primal simplex, it is possible to identify a subproblem containing all the infeasibilities (corresponding to the given basis) to reduce the IIS work-problem dramatically. Furthermore, it is well known that in the solvable case, then the linear program always has an optimal basic solution. , MOSEK, Gurobi [i think], ECOS, CVXOPT, SeDuMi, SDPT3) to handle infeasible and unbounded problems. Therefore for an unbounded primal $ S_ {D} $ is empty, which is the definition of infeasible. 14. 5. Thus the dual problem must be infeasible. In your case, OSQP thinks the problem is infeasible: Aug 25, 2025 · 8. True. This is also the reason that MathOptInterface defines the DUAL_INFEASIBLE status instead of UNBOUNDED. They can be accessed using: res. If, as it happens in many cases, the problem is infeasible due to an unintended mistake in the formulation or because some individual constraint is too tight, then it is likely that infeasibility can be isolated to a few Case 2: Infeasible primal, feasible dual. primal_feasibility_tolerancedouble (default: 1e-07) Primal feasibility tolerance for ‘highs-ds’. Mar 9, 2024 · With numpy, scipy at versions numpy 1. It is the first available QP solver based on first-order methods able to do so. I have tried to use the following relationship: $Ax+c\leq 0$ (from primal) and $c-Ay\geq 0$ (from dual) then $Ax+c \leq c-Ay$ which gives $Ax\leq -Ay$. optimize import linprog A_ub = np. The outcome of the solver is primal infeasibility. " The output from CSDP shows that the problem is primal feasible (X = 0 X = 0 is a primal feasible solution) but that the primal problem is unbounded. Issue relevant to practical implementation are also discussed, including An infeasible value of the candidate solution is one that exceeds one or more of the constraints. Supply, demand and cost of transportation per unit are given in Fig Lecture 15 Primal-dual interior-point method primal-dual central path equations infeasible primal-dual method Jul 28, 2023 · In general, there is no guarantee that a solver will find an infeasibility certificate for an infeasible or unbounded problem. The same optimizer is used for quadratic optimization problems which are internally reformulated to conic form. These methods have performed small to medium sized SDP’s. Duality theory states that: If the primal is unbounded, then the dual is infeasible; If the dual is unbounded, then the primal is infeasible. mps AND Infeasible3. The solver could have stopped for any number of reasons, and only termination_status can tell you why. However, primal–dual codes have had arger problems because of t aper we Apr 1, 1995 · In this paper, we design an algorithm for solving linear semi-infinite programming problems by using the recently developed primal-dual infeasible-interior-point method for linear programming. A certificate of primal infeasibility is a feasible solution to the modified dual The original poster seems to misunderstand the distinction between "primal infeasible" and "dual infeasible. 3. Feb 20, 2020 · We present a general-purpose solver for convex quadratic programs based on the alternating direction method of multipliers, employing a novel operator splitting technique that requires the solution of a quasi-definite linear system with the same coefficient matrix at almost every iteration. Embeddable It has an easy interface to generate customized embeddable C code with no memory manager required. Similarly, when a linear program is primal or dual infeasible then by Farkas’s Lemma a certificate of the infeasible status Dec 4, 2024 · Figure 1: Graphical Representation of Duality If the primal is unbounded, then the dual is infeasible If the dual is unbounded, then the primal is infeasible Strong Duality Theorem If the primal solution has an optimal solution then the dual problem has an optimal solution such that Sep 19, 2018 · OSQP reports that the problem is primal infeasible. Note that Mosek reported dual infeasible, but it was provided the dual problem by CVX, so that corresponds to primal infeasible, which is what CVX reported. 3 Applications 11. FWIW this only appears to happen when the feasible region is a singleton. After pivot Suppose the primal minimization program is unbounded. If you find an infeasible constraint (s), you can try solving a new problem which minimizes the infeasibility (ies) instead of your actual objective function, and still subject to the other constraints. 1 The homogeneous primal-dual problem ¶ The interior-point optimizer is an implementation of the so-called homogeneous and self-dual Jan 31, 2023 · The error statements are like, HiGHS Status 8: model_status is Infeasible; primal_status is At lower/fixed bound or HiGHS Status 8: model_status is Infeasible; primal_status is Basic. Solution status Jan 24, 2017 · I am using GAMS for solving a MILP problem which includes binary variables. Oct 9, 2020 · The solver will stop when the primal and dual residuals are small enough relative to the size of your problem data, with the relative tolerance set by the eps_tol parameter. Show that the optimal dual cost is +oo. An Example. 11 Retrieving infeasibility certificates ¶ When a continuous problem is declared as primal or dual infeasible, MOSEK provides a Farkas-type infeasibility certificate. In the dual problem, the dual vector multiplies the constraints that determine the positions of the constraints in the primal. When the linear program CPLEX solves is infeasible, the associated dual linear program has an unbounded ray. But r0b ¡ ct0 < 0 implies ct0 > r0b contradicting weak duality. e. Sep 18, 2018 · ECOS correctly identifies every LP relaxation as infeasible. 2. Nov 7, 2023 · I am running a model using pulp CBC and have few constraints in the model that may make the model infeasible if wrong input is given to the model. Aug 25, 2025 · As an example of a primal infeasible problem consider minimizing the cost of transportation between a number of production plants and stores: Each plant produces a fixed number of goods, and each store has a fixed demand that must be met. optimize. Thus there are four possibilities 21. That is all solutions $ S_ {D} $ to dual give objective value greater than any primal solution. Question: Exercise 4. However, this does not seem to be possible since we only have constraints on the control inputs u. linprog call, import numpy as np from scipy. More precisely, if the problem appears to be primal infeasible, it will solve the closest primal feasible problem in \f$\ell_2\f$ sense, and (x,y,z) will satisfy. 1 Understanding optimizer log ¶ The optimizer produces a log which splits roughly into four sections: summary of the input data, presolve and other pre-optimize problem setup stages, actual optimizer iterations, solution summary. By weak duality, the corresponding dual problem is infeasible. The original LP is called the primal problem. please help me fix this error The minimum of this and primal_feasibility_tolerance is used for the feasibility tolerance of ‘highs-ipm’. LP Duality In Lecture #3 we saw the Max- ow Min-cut Theorem which stated that the maximum ow from a source to a sink through a graph is always equal to the minimum capacity which needs to be removed from the edges of the graph to disconnect the source and the sink. The model is quite big what probably causes the the problem. The inaccurate statuses define when the optimality, primal infeasibility or dual infeasibility conditions are satisfied with tolerances 10 times larger than the ones set. If, as it happens in many cases, the problem is infeasible due to an unintended mistake in the formulation or because some individual constraint is too tight, then it is likely that infeasibility can be isolated to a few Jan 1, 2021 · Fails (primal infeasible due to numerical-issues) Analysis You won't be able to solve these numerical-issues by increasing iteration-limits only More complex tuning of feasibility-tolerances and co. The solution to the dual problem can be recovered from the final primal solution, and vice versa. would be needed! Transformation / Fixing Can we make those solvers work? I think so. For the Apr 28, 2020 · Mathematical Programs can be unbounded or infeasible. -> Your SOS problem is probably infeasible (SOS is dualized). When I try to solve using MOSEK, it says that the problem is primal infeasible. Oct 17, 2019 · Note: although unbounded primal is sufficient for an infeasible dual, it is not a necessary condition. 2 Locating primal infeasibility ¶ As an example of a primal infeasible problem consider minimizing the cost of transportation between a number of production plants and stores: Each plant produces a fixed number of goods, and each store has a fixed demand that must be met. If removing one primal constraint makes the primal problem unbounded, the dual becomes infeasible (weak duality). 1 Primal-Dual Algorithms So far, we have seen many algorithms based on linear program (LP) relaxations, typically involving rounding a given fractional LP solution to an integral solution of approximately the same objective value. Mar 29, 2017 · By definition these inequalities place an upper bound on our primal. Start of by paying attention to scaling, as evidenced by Mosek;'s warnings. We also discuss the behavior of path-following methods as applied to infeasible problems. level — solution values for the variables. Duality Theory Every LP is associated with another LP, called the dual (in this case, the original LP is called the primal). Use raw_status to get a solver-specific string explaining why the optimization stopped: If the problem is primal infeasible, the certificate is stored in solver->solution->prim_inf_cert If the problem is dual infeasible, the certificate is stored in solver->solution->dual_inf_cert 12. The detailed output follows: - Sep 29, 2020 · 除了数据精度等问题外， MOSEK 优化器会提示下面几种无解情况： PRIME INFEASIBLE DUAL INFEASIBLE 当然有时候两个都 INFEASIBLE。其中 PRIME INFEASIBULE 主要是指限制条件互相冲突了，没有可行解。DUAL INFEASIBLE 是指对偶形式的限制条件。 DUAL INFEASIBLE 通常表明在给定限制条件下，目标函数的方向反了，最优值可能 Status values and errors Status values These are the exit statuses, their respective constants and values returned by the solver as defined in osqp_api_constants. 1. A certificate of dual infeasibility is an improving ray of the primal problem. 1) has an optimal solution, is primal infeasible or is dual infeasible, the optimization algorithm must deal with all three situations. This immediately implies that the dual must be infeasible. cc:317] piecewise jerk path optimizer failed Jun 4, 2025 · 6. 4 Retrieving solution values ¶ After the meaning and quality of the solution (or certificate) have been established, we can query for the actual numerical values. This paper proposes a step length rule with which the algorithm takes large distinct step lengths in the primal and dual spaces and Sep 1, 2018 · Try removing or relaxing constraints until the model becomes feasible. We start with a primal feasible solution and try to reach dual feasibility while maintaining complementary slackness. Supply, demand and cost of transportation per unit are given in Fig So if we have a linear program in maximization linear form, which we are going to call the primal linear program, its dual is formed by having one variable for each constraint of the primal (not counting the non-negativity constraints of the primal variables), and having one constraint for each variable of the primal (plus the non-negative constraints of the dual variables); we change Mar 31, 2016 · If the primal and dual are both infeasible (a pathological case, but can happen), I think bounding the primal (which is already trivially bounded: the empty set fits into any hyperrectangle) will not help. Feb 20, 2025 · When calling Gurobi by pyomo, if the primal is infeasible, how to find a random dual extreme points and extreme ray without coding the dual? A primal infeasibility certi cate indicates a primal infeasible model and the certi cate is reported in the marginals of the equations in the listing le. Supply, demand and cost of transportation per unit are given in Fig Jan 26, 2022 · hello all, i've encountered this problem when osqp returned "primal infeasible" with following log, and i found the solution becomes larger along iterations and fails to converge. 11 Strong duality holds for LPs, except when both primal and dual problems are infeasible, in which f? = 1 and g? = 1 . Could you please make sure, If it is feasible for your vehicle to make that turn (or say if the turning is too sharp to follow)? An infeasible, but first phase optimal primal solution typically speeds up the solution of the relaxed problem. Sep 20, 2024 · 文章浏览阅读761次，点赞3次，收藏2次。只要在设置OSQP参数设置没什么明显错误的情况下，result都会是OsqpEigen::ErrorExitFlag::NoError，即使这个解已经明显违反了约束。不满足约束的解往往是不能用的，那么为了检测约束违反情况，可以使用solver. dobjval — the primal and dual objective value. The primal infeasibility certi cate for a minimization problem Aug 25, 2025 · 9. Applying the same logic to its dual problem, s Corollary 11. 11. One feasible solution would be u[:,t]=0 for all t. You can try to diagnose the cause of the infeasibility, attempt to repair the infeasibility, or both. A certificate of primal infeasibility is a feasible solution to the modified dual Oct 14, 2019 · Your problem has been assesses as primal infeasible (dual infeasibility reported by Mosek refers to the dual problem which CVX provided it). 681439 323874 piecewise_jerk_problem. SCS and CVXOPT don't have any trouble with either version. Nov 2, 2022 · Was this needed to achieve correct behavior in other settings? I have been running into instances in which OSQP is telling me the problem is primal infeasible when a feasible point clearly exists, and the returned primal infeasibility certificate is also incorrect. The unboundedness criterion in the primal simplex algorithm is that the vector B−1Aj is nonpositive for a negative reduced cost ̄cj . I'm using sparse matrices. primalObjValue , Model. It also provides insights into the so called sensitivity analysis. 1 Primal Infeasible Problems ¶ If the problem (12. cc:105] failed optimization status: primal infeasible E0227 18:00:43. Oct 25, 2023 · I am trying to implement MPC to track a reference trajectoy, but I always get a primal infeasible once I set the lower bound of one of the states >0. 15729144, 0. The exact problem status will indicate the type of infeasibility. Dual Simplex Method When: dual feasible, primal infeasible (i. The primal feasibility tolerance controls how primal constraints are evaluated. Instead of minimizing sum of squares, let's minimize the l2 Sep 18, 2024 · For the NaN case, you must always check is_solved_and_feasible (or termination_status and primal_status) before querying the solution. Variants are frequently used in approximation algorithms for NP hard problems that can be formulated as integer programs. Library-free Aug 25, 2025 · 6. 3 Conic Optimization - Interior-point optimizer ¶ For conic optimization problems only an interior-point type optimizer is available. How to check if a Dual LP is infeasible? Get the Dual LP, check if it is feasible by looking for z + A^T y ≥ c If min z > 0, it is infeasible, then the Primal LP is either: Infeasible (we already excluded this in the first step) - Unbounded (Has no optimal) If it is feasible, then the Primal LP is: - Bounded (Has an optimal) Nov 13, 2023 · -> Solver reported unboundness of the dual problem. 0 the following scipy. We observe that the dual of the dual problem is the primal. 12 Retrieving infeasibility certificates ¶ When a continuous problem is declared as primal or dual infeasible, MOSEK provides a Farkas-type infeasibility certificate. This typically happens if such a ray is detected at presolve (note the Presolve: Primal infeasible or unbounded in the log), and only guarantees that the dual problem is infeasible. Apr 13, 2022 · If it is still reported as infeasible, follow the advice in the link. Throughout the process we maintain primal feasibility and drive toward dual feasibility. Varying the dual vector in the dual problem is equivalent to revising the upper bounds in the primal problem. We prove that strict infeasibility (primal or dual) can be detected in O( ln ) iterations, where ρ· is a primal or dual infeasibility measure. Suppose that all entries in the ith row in the tableau (other than xB (j)) are nonnegative. Oct 11, 2021 · Hello all, I have a moderate-sized LP with ~13k variables and ~25k constraints. Jul 3, 2025 · 7. Nov 30, 2024 · This is particularly useful when the primal solution becomes infeasible (e. Perhaps huge objective, evidenced in SCS solution, coupled into constraints in presolve, or as part of CVXPY formulation, causing Mosek to think original problem is primal Primal infeasible problems if p⋆ = +∞ then d⋆ = +∞ or d⋆ = −∞ proof: if primal is infeasible, then from page 5–2, there exists w such that 0, ≥ w AT w = 0, bT w < 0 Jun 19, 2024 · When the solver is ipm and presolve is disabled, the primal_solution_status is reported as feasible when the model status is infeasible. A unified treatment of superlinear convergence, finite termination, and detection of infeasible problems is presented. The weak duality Aug 25, 2025 · 14. Once the optimal solution to the relaxed problem is identified (and is automatically projected back to the original problem space), it may be used by the modeler to modify the problem in order to become feasible. 3 (Debugging infeasibility). In this tutorial we show how to analyze the most important parts of the log when initially debugging a model: input data (1) and solution summary (4). ) Weak duality shows that if the primal or dual is unbounded then the other must be infeasible. y, res. xx — solution values for the variables. According to [BGSB19, Thm. The proposed algorithm enjoys the advantages of having “multiple inexactness” and “warm start” for computational efficiency. 2 Automatic Repair of Infeasible Problems ¶ MOSEK provides an automatic repair tool for infeasible linear problems which we cover in this section. I set up the initial OSQP instance using a "fully occupied" structure matrix A, with 1's in every location where a nonzero value could potentially be, zeros elsewhere. If you just want a primal feasible solution and don't care about the Apr 1, 2024 · The INFEASIBLE_OR_UNBOUNDED status means that a primal unbounded ray has been found, but the solver does not have a primal-feasible solution. Aug 25, 2025 · 12. 1) is infeasible (has no feasible solution), MOSEK will report a certificate of primal infeasibility: The dual solution reported is the certificate of infeasibility, and the primal solution is undefined. (= Weak Duality Theorem Primal infeasible, dual unbounded (no gap). The method achieves robust convergence rates and Jul 11, 2023 · Did you still get 'Infeasible' status with Infeasible1. Aug 25, 2025 · For continuous problems and when the solver is run with default parameters, the feasibility status should ideally be prosta. For example, in some cases that can prove infeasibility during preserve without generating a certificate. Aug 25, 2025 · 7. To see this in the rst case, let y be any feasible solution to the dual. 1 Automatic repair Jul 27, 2020 · Mosek solved the dual (you didn’ show that beginning part of the output), and concluded it is dual infeasible; therefore, CVX reported it is (primal) infeasible. This relationship is important for proper interpretation of infeasible solution output. g. array( [[-0. This must be true for the primal since any feasible solution to the dual would provide an upper bound on the primal objective function by the weak duality theorem; this contradicts the fact that Aug 25, 2025 · primal/dual infeasible — the problem is infeasible or unbounded or a combination of those. Is there a way to fi Aug 25, 2025 · primal/dual infeasible — the problem is infeasible or unbounded or a combination of those. Thus, (4) has no solution and hence (1) has solution. (This will be a homework problem. However there is a problem in the solution. If, as it happens in many cases, the problem is infeasible due to an unintended mistake in the formulation or because some individual constraint is too tight, then it is likely that infeasibility can be isolated to a few Abstract. julia> using HiGHS julia> begin data = """ NAME ROWS N NoObj Dec 16, 2022 · Dual feasibility is tied to primal boundedness. In general if a linear program has an optimal solution, then a primal and dual optimal solution is a certificate of the solvable status. For the Nov 3, 2018 · I understand that with the strong duality theorem, the dual LP is infeasible when primal is unbounded (ex: linear programming infeasibility, dual & primal relation). npuo smfben anhv ibzsfjjh vupjr fevurmr gcd parpmdo zlng uunjq