Le Thi Hoai An: "DC Programming for solving a class of global optimization problems via reformulation by exact penalty".

Abstract: 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.

 
Keywords: d.c. programming, polyhedral d.c. programming, DCA, combined DCA - branch and bound algorithm, reformulations, exact penalty.

Citation: Le Thi Hoai An, DC Programming for solving a class of global optimization problems via reformulation by exact penalty, in “Global Constrained Optimization and Constraint Satisfaction”, Lecture Note in Computer Science Volum 2861 (2003), pp. 87-101.