Unified global optimality conditions for smooth minimization problems with mixed variables
Department of Applied Mathematics, University of New South
Wales, Sydney 2052, Australia; email@example.com, firstname.lastname@example.org
2 Hanoi Pedagogical University No. 2, Vinh Phuc, Vietnam.
Accepted: 4 December 2007
In this paper we establish necessary as well as sufficient conditions for a given feasible point to be a global minimizer of smooth minimization problems with mixed variables. These problems, for instance, cover box constrained smooth minimization problems and bivalent optimization problems. In particular, our results provide necessary global optimality conditions for difference convex minimization problems, whereas our sufficient conditions give easily verifiable conditions for global optimality of various classes of nonconvex minimization problems, including the class of difference of convex and quadratic minimization problems. We discuss numerical examples to illustrate the optimality conditions
Mathematics Subject Classification: 90C30 / 90C45
Key words: Nonconvex optimization / global optimization / optimality conditions / discrete constraints / box constraints / difference of convex functions / quadratic minimization.
© EDP Sciences, ROADEF, SMAI, 2008