Sometimes, the feasible set of an optimization problem that one aims to solve using a Nonlinear Programming algorithm is empty. In this case, two characteristics of the algorithm are desirable. On the one hand, the algorithm should converge to a minimizer of some infeasibility measure. On the other hand, one may wish to find a point with minimal infeasibility for which some optimality condition...

We discuss some properties of the distance to infeasibility of a conic linear system Ax = b; x 2 C; where C is a closed convex cone. Some interesting connections between the distance to infeasibility and the solution of certain optimization problems are established. Such connections provide insight into the estimation of the distance to infeasibility and the explicit computation of infeasible p...

Article history: Available online 20 August 2013 MSC: 03B45 03B60 03F07 68Q17

Infeasibility resolution is an important aspect of infeasibility analysis. This paper proposes a multi-objective programming model for infeasibility resolution and develops a method based on l ∞ norm goal programming to solve the problem. Any solution is at least weakly efficient and any efficient solution is reachable by regulating the weights. For the special case of irreducibly inconsistent ...

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Detecting infeasibility in conic optimization and providing certificates for infeasibility pose a bigger challenge than in the linear case due to the lack of strong duality. In this paper we generalize the approximate Farkas lemma of Todd and Ye [12] from the linear to the general conic setting, and use it to propose stopping criteria for interior point algorithms using self-dual embedding. The...

Context: Automatic code-based test input generation aims at generating a test suite ensuring good code coverage. Dynamic Symbolic Execution (DSE) recently emerged as a strong code-based testing technique to increase coverage by solving path conditions with a combination of symbolic constraint solving and concrete executions. Objective: When selecting paths in DSE for generating test inputs, som...