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Unified global optimalityconditionsfor 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 assufficient conditions for a given feasible point to be a globalminimizer of smooth minimization problems with mixed variables.These problems, for instance, cover box constrained smooth minimizationproblems and bivalent optimization problems. In particular, ourresults provide necessary global optimality conditions for differenceconvex minimization problems, whereas our sufficient conditionsgive easily verifiable conditions for global optimality of variousclasses of nonconvex minimization problems, including the class ofdifference of convex and quadratic minimization problems. Wediscuss numerical examples to illustrate the optimalityconditions

Keywords

Nonconvex optimizationglobal optimizationoptimality conditionsdiscrete constraintsbox constraintsdifference of convex functionsquadraticminimization.
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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