• Title/Summary/Keyword: -semilocally preinvex

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VECTOR OPTIMIZATION INVOLVING GENERALIZED SEMILOCALLY PRE-INVEX FUNCTIONS

  • GUPTA, SUDHA;SHARMA, VANI;CHAUDHARY, MAMTA
    • Journal of applied mathematics & informatics
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    • v.33 no.3_4
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    • pp.235-246
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    • 2015
  • In this paper, a vector optimization problem over cones is considered, where the functions involved are $\eta$-semidifferentiable. Necessary and sufficient optimality conditions are obtained. A dual is formulated and duality results are proved using the concepts of cone $\rho$-semilocally preinvex, cone $\rho$-semilocally quasi-preinvex and cone $\rho$-semilocally pseudo-preinvex functions.

OPTIMALITY CONDITIONS AND DUALITY FOR SEMI-INFINITE PROGRAMMING INVOLVING SEMILOCALLY TYPE I-PREINVEX AND RELATED FUNCTIONS

  • Jaiswal, Monika;Mishra, Shashi Kant;Al Shamary, Bader
    • Communications of the Korean Mathematical Society
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    • v.27 no.2
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    • pp.411-423
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    • 2012
  • A nondifferentiable nonlinear semi-infinite programming problem is considered, where the functions involved are ${\eta}$-semidifferentiable type I-preinvex and related functions. Necessary and sufficient optimality conditions are obtained for a nondifferentiable nonlinear semi-in nite programming problem. Also, a Mond-Weir type dual and a general Mond-Weir type dual are formulated for the nondifferentiable semi-infinite programming problem and usual duality results are proved using the concepts of generalized semilocally type I-preinvex and related functions.