• Title/Summary/Keyword: invexity

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ON SUFFICIENT OPTIMALITY THEOREMS FOR NONSMOOTH MULTIOBJECTIVE OPTIMIZATION PROBLEMS

  • Kim, Moon-Hee;Lee, Gue-Myung
    • Communications of the Korean Mathematical Society
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    • v.16 no.4
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    • pp.667-677
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    • 2001
  • We consider a nonsmooth multiobjective opimization problem(PE) involving locally Lipschitz functions and define gen-eralized invexity for locally Lipschitz functions. Using Fritz John type optimality conditions, we establish Fritz John type sufficient optimality theorems for (PE) under generalized invexity.

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MULTIOBJECTIVE VARIATIONAL PROGRAMMING UNDER GENERALIZED VECTOR VARIATIONAL TYPE I INVEXITY

  • Kim, Moon-Hee
    • Communications of the Korean Mathematical Society
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    • v.19 no.1
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    • pp.179-196
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    • 2004
  • Mond-Weir type duals for multiobjective variational problems are formulated. Under generalized vector variational type I invexity assumptions on the functions involved, sufficient optimality conditions, weak and strong duality theorems are proved efficient and properly efficient solutions of the primal and dual problems.

OPTIMALITY AND DUALITY FOR NONDIFFERENTIABLE FRACTIONAL PROGRAMMING WITH GENERALIZED INVEXITY

  • Kim, Gwi Soo;Kim, Moon Hee
    • Journal of the Chungcheong Mathematical Society
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    • v.29 no.3
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    • pp.465-475
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    • 2016
  • We establish necessary and sufficient optimality conditions for a class of generalized nondifferentiable fractional optimization programming problems. Moreover, we prove the weak and strong duality theorems under (V, ${\rho}$)-invexity assumption.

OPTIMALITY AND DUALITY IN NONSMOOTH VECTOR OPTIMIZATION INVOLVING GENERALIZED INVEX FUNCTIONS

  • Kim, Moon-Hee
    • Journal of applied mathematics & informatics
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    • v.28 no.5_6
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    • pp.1527-1534
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    • 2010
  • In this paper, we consider nonsmooth optimization problem of which objective and constraint functions are locally Lipschitz. We establish sufficient optimality conditions and duality results for nonsmooth vector optimization problem given under nearly strict invexity and near invexity-infineness assumptions.

SYMMETRIC DUALITY FOR NONLINEAR MIXED INTEGER PROGRAMS WITH A SQUARE ROOT TERM

  • Kim, Do-Sang;Song, Young-Ran
    • Journal of the Korean Mathematical Society
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    • v.37 no.6
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    • pp.1021-1030
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    • 2000
  • We formulate a pair of symmetric dual mixed integer programs with a square root term and establish the weak, strong and converse duality theorems under suitable invexity conditions. Moreover, the self duality theorem for our pair is obtained by assuming the kernel function to be skew symmetric.

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MIXED TYPE DUALITY FOR A PROGRAMMING PROBLEM CONTAINING SUPPORT FUNCTION

  • Husain, I.;Jabeen, Z.
    • Journal of applied mathematics & informatics
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    • v.15 no.1_2
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    • pp.211-225
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    • 2004
  • A mixed type dual to a programming problem containing support functions in a objective as well as constraint functions is formulated and various duality results are validated under generalized convexity and invexity conditions. Several known results are deducted as special cases.