In this paper we consider correcting infeasibility in a second order conic linear inequality by minimal changes in the problem data. Under certain conditions, it is proved that the minimal correction can be done by solving a lower dimensional convex problem. Finally, several examples are presented to show the efficiency of the new approach.

This document briefly describes our freely distributed Maple library spectra, for Semidefinite Programming solved Exactly with Computational Tools of Real Algebra. It solves linear matrix inequalities in exact arithmetic and it is targeted to small-size, possibly degenerate problems for which symbolic infeasibility or feasibility certificates are required.

3 Polynomial Optimization, Sums of Squares, and Applications 47 Pablo A. Parrilo 3.1 Nonnegative Polynomials and Sums of Squares . . . . . . . . . . 48 3.2 Applications of Sum of Squares Programs . . . . . . . . . . . . . 76 3.3 Special Cases and Structure Exploitation . . . . . . . . . . . . . 86 3.4 Infeasibility Certificates . . . . . . . . . . . . . . . . . . . . . . . 106 3.5 Duality and S...

We describe a simple adaptive memory search method for Boolean Optimization Problems. The search balances the level of infeasibility against the quality of the solution, and uses a simple dynamic tabu search mechanism. Computational results on a portfolio of test problems taken from the literature are reported, showing very favorable results, both in terms of search speed and solution quality.

High school timetabling (HST) is a well-known real-world combinatorial optimisation problem. It requires the scheduling of events and resources, such as courses, classes of students, teachers, rooms and more within a fixed number of time slots subject to a set of constraints. In a standard fashion, constraints are separated into ‘hard’ and soft. The hard constraints must be satisfied in order t...

We prove local and global convergence results for an interior-point methodapplied to mathematical programs with equilibrium constraints. The globalresult shows the algorithm minimizes infeasibility regardless of startingpoint, while one result proves local convergence when penalty functions areexact; another local result proves convergence when the solution is not evena KKT point.

Metric regularity is a central concept in variational analysis for the study of solution mappings associated with “generalized equations”, including variational inequalities and parameterized constraint systems. Here it is employed to characterize the distance to irregularity or infeasibility with respect to perturbations of the system structure. Generalizations of the Eckart-Young theorem in n...

Using a direct counting argument, we derive lower and upper bounds for the number of nodes enumerated by linear programming-based branch-and-bound (B&B) method to prove the infeasibility of an integer knapsack problem. We prove by example that the size of the B&B tree could be exponential in the worst case.