Unified global optimality conditions for smooth minimization problems with mixed variables

Vaithilingam Jeyakumar; Sivakolundu Srisatkunarajah; Nguyen Quang Huy

RAIRO - Operations Research (2008)

  • Volume: 42, Issue: 3, page 361-370
  • ISSN: 0399-0559

Abstract

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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

How to cite

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Jeyakumar, Vaithilingam, Srisatkunarajah, Sivakolundu, and Huy, Nguyen Quang. "Unified global optimality conditions for smooth minimization problems with mixed variables." RAIRO - Operations Research 42.3 (2008): 361-370. <http://eudml.org/doc/250403>.

@article{Jeyakumar2008,
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 },
author = {Jeyakumar, Vaithilingam, Srisatkunarajah, Sivakolundu, Huy, Nguyen Quang},
journal = {RAIRO - Operations Research},
keywords = {Nonconvex optimization; global optimization; optimality conditions; discrete constraints; box constraints; difference of convex functions; quadratic minimization.; nonconvex optimization; global optimization; box constraints; quadratic minimization},
language = {eng},
month = {8},
number = {3},
pages = {361-370},
publisher = {EDP Sciences},
title = {Unified global optimality conditions for smooth minimization problems with mixed variables},
url = {http://eudml.org/doc/250403},
volume = {42},
year = {2008},
}

TY - JOUR
AU - Jeyakumar, Vaithilingam
AU - Srisatkunarajah, Sivakolundu
AU - Huy, Nguyen Quang
TI - Unified global optimality conditions for smooth minimization problems with mixed variables
JO - RAIRO - Operations Research
DA - 2008/8//
PB - EDP Sciences
VL - 42
IS - 3
SP - 361
EP - 370
AB - 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
LA - eng
KW - Nonconvex optimization; global optimization; optimality conditions; discrete constraints; box constraints; difference of convex functions; quadratic minimization.; nonconvex optimization; global optimization; box constraints; quadratic minimization
UR - http://eudml.org/doc/250403
ER -

References

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  14. M.C. Pinar and M. Teboulle, On semidefinite bounds for maximization of a non-convex quadratic objective over l1 unit ball. RAIRO Oper. Res.40 (2006) 253–265.  
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