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

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.


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