• 제목/요약/키워드: sufficient optimality conditions

검색결과 34건 처리시간 0.029초

THE KARUSH-KUHN-TUCKER OPTIMALITY CONDITIONS IN INTERVAL-VALUED MULTIOBJECTIVE PROGRAMMING PROBLEMS

  • Hosseinzade, Elham;Hassanpour, Hassan
    • Journal of applied mathematics & informatics
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    • 제29권5_6호
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    • pp.1157-1165
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    • 2011
  • The Karush-Kuhn-Tucker (KKT) necessary optimality conditions for nonlinear differentiable programming problems are also sufficient under suitable convexity assumptions. The KKT conditions in multiobjective programming problems with interval-valued objective and constraint functions are derived in this paper. The main contribution of this paper is to obtain the Pareto optimal solutions by resorting to the sufficient optimality condition.

ON SUFFICIENT OPTIMALITY THEOREMS FOR NONSMOOTH MULTIOBJECTIVE OPTIMIZATION PROBLEMS

  • Kim, Moon-Hee;Lee, Gue-Myung
    • 대한수학회논문집
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    • 제16권4호
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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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GLOBAL PARAMETRIC SUFFICIENT OPTIMALITY CONDITIONS FOR DISCRETE MINMAX FRACTIONAL PROGRAMMING PROBLEMS CONTAINING GENERALIZED $({\theta},\;{\eta},\;{\rho})-V-INVEX$ FUNCTIONS AND ARBITRARY NORMS

  • Zalmai, G.J.
    • Journal of applied mathematics & informatics
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    • 제23권1_2호
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    • pp.1-23
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    • 2007
  • The purpose of this paper is to develop a fairly large number of sets of global parametric sufficient optimality conditions under various generalized $({\theta},\;{\eta},\;{\rho})-V-invexity$ assumptions for a discrete minmax fractional programming problem involving arbitrary norms.

NECESSARY AND SUFFICIENT OPTIMALITY CONDITIONS FOR FUZZY LINEAR PROGRAMMING

  • Farhadinia, Bahram
    • Journal of applied mathematics & informatics
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    • 제29권1_2호
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    • pp.337-349
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    • 2011
  • This paper is concerned with deriving necessary and sufficient optimality conditions for a fuzzy linear programming problem. Toward this end, an equivalence between fuzzy and crisp linear programming problems is established by means of a specific ranking function. Under this setting, a main theorem gives optimality conditions which do not seem to be in conflict with the so-called Karush-Kuhn-Tucker conditions for a crisp linear programming problem.

NECESSARY AND SUFFICIENT OPTIMALITY CONDITIONS FOR CONTROL SYSTEMS DESCRIBED BY INTEGRAL EQUATIONS WITH DELAY

  • Elangar, Gamal-N.;Mohammad a Kazemi;Kim, Hoon-Joo
    • 대한수학회지
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    • 제37권4호
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    • pp.625-643
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    • 2000
  • In this paper we formulate an optimal control problem governed by time-delay Volterra integral equations; the problem includes control constraints as well as terminal equality and inequality constraints on the terminal state variables. First, using a special type of state and control variations, we represent a relatively simple and self-contained method for deriving new necessary conditions in the form of Pontryagin minimum principle. We show that these results immediately yield classical Pontryagin necessary conditions for control processes governed by ordinary differential equations (with or without delay). Next, imposing suitable convexity conditions on the functions involved, we derive Mangasarian-type and Arrow-type sufficient optimality conditions.

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OPTIMALITY AND DUALITY IN NONSMOOTH VECTOR OPTIMIZATION INVOLVING GENERALIZED INVEX FUNCTIONS

  • Kim, Moon-Hee
    • Journal of applied mathematics & informatics
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    • 제28권5_6호
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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.