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Unified global optimalityconditions for smooth minimization problems with mixed variables

Published online by Cambridge University Press:  20 August 2008

Vaithilingam Jeyakumar ,
Sivakolundu Srisatkunarajah  and
Nguyen Quang Huy
Vaithilingam Jeyakumar
Affiliation:
Department of Applied Mathematics, University of New South Wales, Sydney 2052, Australia; jeya@maths.unsw.edu.au, sri@maths.unsw.edu.au
Sivakolundu Srisatkunarajah
Affiliation:
Department of Applied Mathematics, University of New South Wales, Sydney 2052, Australia; jeya@maths.unsw.edu.au, sri@maths.unsw.edu.au
Nguyen Quang Huy
Affiliation:
Department of Applied Mathematics, University of New South Wales, Sydney 2052, Australia; jeya@maths.unsw.edu.au, sri@maths.unsw.edu.au Hanoi Pedagogical University No. 2, Vinh Phuc, Vietnam.
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Abstract

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

Keywords

Nonconvex optimizationglobal optimizationoptimality conditionsdiscrete constraintsbox constraintsdifference of convex functionsquadratic minimization.
Type
Research Article
Information
RAIRO - Operations Research , Volume 42 , Issue 3 , July 2008 , pp. 361 - 370
Copyright
© EDP Sciences, ROADEF, SMAI, 2008

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