LAGRANGIAN-DUALITY OF CONCAVE MINIMIZATION SUBJECT TO LINEAR CONSTRAINTS AND AN ADDITIONAL FACIAL REVERSE CONVEX CONSTRAINT

This paper is concerned with the global optimization problem of minimi zing a concave function subject to linear constraints and an additiona l facial reverse convex constraint. Here, the feasible set is the unio n of some faces of the polyhedron determined by the linear constraints . Several well-known mathematical problems can be written or transform ed into the form considered. The paper addresses the Lagrangian dualit y of the problem. It is shown that, under slight assumptions, the dual ity gap can be closed with a finite dual multiplier. Finite methods ba sed on solving concave minimization problems are also proposed. We dea l with the advantages accrued when outer approximation, cutting plane, or branch-and-bound methods are used for solving these subproblems.