Canonical dual approach to solving 0-1 quadratic programming problems. (English) Zbl 1180.90195

Fang, Shu-Cherng; Gao, David Yang; Sheu, Ruey-Lin; Wu, Soon-Yi

J. Ind. Manag. Optim. 4, No. 1, 125-142 (2008).

Summary: By using the canonical dual transformation developed recently, we derive a pair of canonical dual problems for 0-1 quadratic programming problems in both minimization and maximization form. Regardless convexity, when the canonical duals are solvable, no duality gap exists between the primal and corresponding dual problems. Both global and local optimality conditions are given. An algorithm is presented for finding global minimizers, even when the primal objective function is not convex. Examples are included to illustrate this new approach.

MSC:

90C09	Boolean programming
90C20	Quadratic programming
49N15	Duality theory (optimization)
49M37	Numerical methods based on nonlinear programming
90C26	Nonconvex programming, global optimization

Keywords:

global optimization; duality; NP-hard problems