Hit-and run algorithms for the identification of nonredundant linear inequalities
Mathematical Programming: Series A and B
Hit-and-run algorithms for generating multivariate distributions
Mathematics of Operations Research
SIAM Review
Presolving in linear programming
Mathematical Programming: Series A and B
The Constraint Consensus Method for Finding Approximately Feasible Points in Nonlinear Programs
INFORMS Journal on Computing
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We present a constraint analysis methodology for linear matrix inequality 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 sampled point. Thus, an implementation requires a method to collect points in the ambient space and a constraint oracle. Much of this paper will be devoted to the development of a hit-and-run sampling methodology. Test results confirm that our approach not only provides information required for constraint analysis but will also, if the feasible region has a nonvoid interior, with probability one, find a feasible point.