Abstract

Concave minimization over a bounded polyhedral convex set with an additional reverse convex constraint contains important problems in non-convex programming. Both theoretical and practical studies ofthis class ofnon-convex programs can be made more convenient and easier when the reverse convex constraint is penalized. We have proved that if the concave function defining the reverse convex constraint is non-negative over bounded polyhedral convex set, then the exact penalty and the stability of the Lagrangian duality hold. Consequently, equivalent difference of convex ((d.c.) functions) programs are formulated