The relationship between the mathematical program with linear complementarity constraints (MPCC) and its inequality relaxation is studied. A new sequential quadratic programming (SQP) method is presented for solving the MPCC based on this relationship. A certain SQP technique is introduced to deal with the possible infeasibility of quadratic programming subproblems. Global convergence results a...

In this article, we present a geometric theoretical analysis of semidefinite feasibility problems (SDFPs). We introduce the concept of hyper feasible partitions and sub-hyper feasible directions, and show how they can be used to decompose SDFPs into smaller ones, in a way that preserves most feasibility properties of the original problem. With this technique, we develop a detailed analysis of w...

1 Significance A method is proposed that either returns all solutions to steady-state models of distillation columns or proves infeasibility. No initial estimates are required. The computational effort grows linearly with the number of stages. Successful solution of a numerically challenging reactive distillation column with 7 steady-states show the robustness of the method. The authors do not ...

The Douglas-Rachford algorithm can be represented as the fixed point iteration of a firmly nonexpansive operator. When operator has no points, algorithm's iterates diverge, but difference between consecutive converges to so-called minimal displacement vector, which used certify infeasibility an optimization problem. In this paper, we establish new properties allow us generalize some existing re...

We present an overview of the essential elements of semidefinite programming as a computational tool for the analysis of systems and control problems. We make particular emphasis on general duality properties as providing suboptimality or infeasibility certificates. Our focus is on the exciting developments occurred in the last few years, including robust optimization, combinatorial optimizatio...

VSDP is a MATLAB software package for rigorously solving semidefinite programming problems. It expresses these problems in a notation closely related to the form given in textbooks and scientific papers. Functions for computing verified forward error bounds of the true optimal value and verified certificates of feasibility and infeasibility are provided. All rounding errors due to floating poin...

This paper presents the design of a novel distributed algorithm d-IRA for the reachability analysis of linear hybrid automata. Recent work on iterative relaxation abstraction (IRA) is leveraged to distribute the computational problem among multiple computational nodes in a non-redundant manner by performing careful infeasibility analysis of linear programs corresponding to spurious counterexamp...

We tackle the problem of finding a smallest-cardinality MUS (SMUS) of a given formula. The SMUS provides a succinct explanation of infeasibility and is valuable for applications that rely on such explanations. We present a branch-and-bound algorithm that utilizes iterative MAXSAT solutions to generate lower and upper bounds on the size of the SMUS, and branch on specific subformulas to find it....

As regards of supper efficiency models which increased the discrimination power of the standard DEA models, still infeasibility may occure. In literature there exists some models overcome this difficulty. In this paper a new procedure has been mooted in order to remove this shortcoming in a way that both input savings and output surplus are being considered. This procedure deals with nonradial ...

Polymorphic malcode remains one of the most troubling threats for information security and intrusion defense systems. The ability for malcode to be automatically transformed into to a semantically equivalent variant frustrates attempts to construct a single, simple, easily verifiable representation. We present a quantitative analysis of the strengths and limitations of shellcode polymorphism an...