Constraint Consensus Methods for Finding Strictly Feasible Points of Linear Matrix Inequalities

Constraint Consensus Methods for Finding Interior Feasible Points in Second-Order Cones

Optimization problems with second-order cone constraints SOCs can be solved efficiently by interior point methods. In order for some of these methods to get started or to converge faster, it is important to have an initial feasible point or near-feasible point. In this paper, we study and apply Chinneck’sOriginal constraint consensus method andDBmax constraint consensus method to find near-feas...

The Constraint Consensus Method for Finding Approximately Feasible Points in Nonlinear Programs

T paper develops a method for moving quickly and cheaply from an arbitrary initial point at an extreme distance from the feasible region to a point that is relatively near the feasible region of a nonlinearly constrained model. The method is a variant of a projection algorithm that is shown to be robust, even in the presence of nonconvex constraints and infeasibility. Empirical results are pres...

Iterative Methods for Equilibrium Problems, Variational Inequalities and Fixed Points

Feasibility and Constraint Analysis of Sets of Linear Matrix Inequalities

We present a constraint analysis methodology for Linear Matrix Inequality (LMI) constraints. If the constraint set is found to be feasible we search for a minimal representation; otherwise, we search for an irreducible infeasible system. The work is based on the solution of a set covering problem where each row corresponds to a sample point and is determined by constraint satisfaction at the sa...

On Boundness Conditions for the Set of Feasible Points of Systems of Linear Inequalities

Abstract In a linear programming problem involving maximization (or minimization) of the objective function the set of feasible points is often required to be bounded above (or below). A criterion based on the simplex method which requires the constraints coefficients of the entering variable to be zero or negative for the set of feasible points to be unbounded is often used. In this paper, the...