D.C. Programming for Solving a Class of Global Optimization Problems via Reformulation by Exact Penalty

摘要

We consider a class of important problems in global optimization, namely concave minimization over a bounded polyhedral convex set with an additional reverse convex constraint. Using a related exact penalty property, we reformulate the class of mixed zero-one concave minimization programs, concave minimization programs over efficient sets, bilevel programs, and concave minimization programs with mixed linear complementarity constraints in the form of equivalent d.c. (difference of convex functions) programs. Solution methods based on d.c. optimization algorithms (DCA) and the combined DCA - branch and bound are investigated.