In semidefinite programming (SDP), unlike in linear programming, Farkas’ lemma may fail to prove infeasibility. Here we obtain an exact, short certificate of infeasibility in SDP by an elementary approach: we reformulate any equality constrained semidefinite system using only elementary row operations, and rotations. When a system is infeasible, the reformulated system is trivially infeasible. ...

Explaining the causes of infeasibility of Boolean formulas has many practical applications in various fields. A small unsatisfiable subformula provides a succinct explanation of infeasibility and is valuable for applications. In recent years the problem of finding unsatisfiable subformulas has been addressed frequently by research works, which are mostly based on the SAT solvers with DPLL backt...

Explaining the causes of infeasibility of Boolean formulas has many practical applications in various fields. We are generally interested in a small explanation of unsatisfiability that excludes irrelevant information. A small unsatisfiable core provides a succinct explanation of infeasibility and is valuable for applications. In recent years the problem of finding unsatisfiable subformulas has...

The perceptron and the von Neumann algorithms were developed to solve Linear Feasibility Problems. In this paper, we investigate and reveal the duality relationship between these two algorithms. The specific forms of Linear Feasibility Problems solved by the perceptron and the von Neumann algorithms are a pair of alternative systems by the Farkas Lemma. A solution of one problem serves as an in...

Presolving for linear programming is an essential ingredient in many commercial packages. This step eliminates redundant constraints and identically zero variables, and it identiies possible infeasibility and unboundedness. In semideenite programming, identically zero variables corresponds to lack of a constraint qualiication which can result in both theoretical and numerical diiculties. A nonz...

Abstract We propose generalizations of reduction pairs, well-established techniques for proving termination term rewriting, in order to prove unsatisfiability reachability (infeasibility) plain and conditional rewriting. adapt the weighted path order, a merger Knuth–Bendix lexicographic into proposed framework. The approach is implemented prover , strength our demonstrated through examples expe...

Farkas’ lemma is a fundamental result from linear programming providing linear certificates for infeasibility of systems of linear inequalities. In semidefinite programming, such linear certificates only exist for strongly infeasible linear matrix inequalities. We provide nonlinear algebraic certificates for all infeasible linear matrix inequalities in the spirit of real algebraic geometry. Mor...

A central result in the theory of integer optimization states that a system of linear diophantine equations Ax = b has no integral solution if and only if there exists a vector in the dual lattice, yT A integral such that yT b is fractional. We extend this result to systems that both have equations and inequalities {Ax = b, Cx ≤ d}. We show that a certificate of integral infeasibility is a line...

The objective of this work is to study weak infeasibility in second order cone programming. For this purpose, we consider a relaxation sequence of feasibility problems that mostly preserve the feasibility status of the original problem. This is used to show that for a given weakly infeasible problem at most m directions are needed to approach the cone, where m is the number of Lorentz cones. We...