Unified global optimality conditions for smooth minimization problems with mixed variables
RAIRO - Operations Research - Recherche Opérationnelle, Tome 42 (2008) no. 3, pp. 361-370.

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

DOI : 10.1051/ro:2008019
Classification : 90C30, 90C45
Mots-clés : nonconvex optimization, global optimization, optimality conditions, discrete constraints, box constraints, difference of convex functions, quadratic minimization 
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     author = {Jeyakumar, Vaithilingam and Srisatkunarajah, Sivakolundu and Huy, Nguyen Quang},
     title = {Unified global optimality conditions for smooth minimization problems with mixed variables},
     journal = {RAIRO - Operations Research - Recherche Op\'erationnelle},
     pages = {361--370},
     publisher = {EDP-Sciences},
     volume = {42},
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     mrnumber = {2444492},
     zbl = {1153.90544},
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     url = {http://www.numdam.org/articles/10.1051/ro:2008019/}
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Jeyakumar, Vaithilingam; Srisatkunarajah, Sivakolundu; Huy, Nguyen Quang. Unified global optimality conditions for smooth minimization problems with mixed variables. RAIRO - Operations Research - Recherche Opérationnelle, Tome 42 (2008) no. 3, pp. 361-370. doi : 10.1051/ro:2008019. http://www.numdam.org/articles/10.1051/ro:2008019/

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