• 제목/요약/키워드: invexity

검색결과 34건 처리시간 0.134초

DUALITY FOR MULTIOBJECTIVE FRACTIONAL CONTROL PROBLEMS WITH GENERALIZED INVEXITY

  • Nahak, C.;Nanda, S.
    • Journal of applied mathematics & informatics
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    • v.5 no.2
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    • pp.475-488
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    • 1998
  • Wolfe and Mond-Weir type duals for multiobjective con-trol problems are formulated. Under pseudo-invexity/quasi-invexity assumptions of the functions involved, weak and strong duality the-orems are proved to relate efficient solutions of the primal and dual problems.

INVEXITY AS NECESSARY OPTIMALITY CONDITION IN NONSMOOTH PROGRAMS

  • Sach, Pham-Huu;Kim, Do-Sang;Lee, Gue-Myung
    • 대한수학회지
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    • v.43 no.2
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    • pp.241-258
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    • 2006
  • This paper gives conditions under which necessary optimality conditions in a locally Lipschitz program can be expressed as the invexity of the active constraint functions or the type I invexity of the objective function and the constraint functions on the feasible set of the program. The results are nonsmooth extensions of those of Hanson and Mond obtained earlier in differentiable case.

CONTINUOUS PROGRAMMING CONTAINING SUPPORT FUNCTIONS

  • Husain, I.;Jabeen, Z.
    • Journal of applied mathematics & informatics
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    • v.26 no.1_2
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    • pp.75-106
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    • 2008
  • In this paper, we derive necessary optimality conditions for a continuous programming problem in which both objective and constraint functions contain support functions and is, therefore, nondifferentiable. It is shown that under generalized invexity of functionals, Karush-Kuhn-Tucker type optimality conditions for the continuous programming problem are also sufficient. Using these optimality conditions, we construct dual problems of both Wolfe and Mond-Weir types and validate appropriate duality theorems under invexity and generalized invexity. A mixed type dual is also proposed and duality results are validated under generalized invexity. A special case which often occurs in mathematical programming is that in which the support function is the square root of a positive semidefinite quadratic form. Further, it is also pointed out that our results can be considered as dynamic generalizations of those of (static) nonlinear programming with support functions recently incorporated in the literature.

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SYMMETRIC DUALITY FOR A CLASS OF NONDIFFERENTIABLE VARIATIONAL PROBLEMS WITH INVEXITY

  • LEE, WON JUNG
    • Journal of the Korean Society for Industrial and Applied Mathematics
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    • v.6 no.1
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    • pp.67-80
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    • 2002
  • We formulate a pair of nondifferentiable symmetric dual variational problems with a square root term. Under invexity assumptions, we establish weak, strong, converse and self duality theorems for our variational problems by using the generalized Schwarz inequality. Also, we give the static case of our nondifferentiable symmetric duality results.

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ON MULTIOBJECTIVE GENERALIZED SYMMETRIC DUAL PROGRAMS WITH $\rho-(\eta,0)$-INVEXITY

  • Nahak, C.
    • Journal of applied mathematics & informatics
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    • v.5 no.3
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    • pp.797-804
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    • 1998
  • A pair of multiobjective generalized symmetric dual non-linear programming problems and weak strong and converse dual-ity theorems for these problems are established under generalized $\rho-(\eta,0)$-invexity assumptions. Several known results are obtained as special cases.

ON VARIATIONAL PROBLEMS INVOLVING HIGHER ORDER DERIVATIVES

  • HUSAIN I.;JABEEN Z.
    • Journal of applied mathematics & informatics
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    • v.17 no.1_2_3
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    • pp.433-455
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    • 2005
  • Fritz John, and Karush-Kuhn-Tucker type optimality conditions for a constrained variational problem involving higher order derivatives are obtained. As an application of these Karush-Kuhn-Tucker type optimality conditions, Wolfe and Mond-Weir type duals are formulated, and various duality relationships between the primal problem and each of the duals are established under invexity and generalized invexity. It is also shown that our results can be viewed as dynamic generalizations of those of the mathematical programming already reported in the literature.

ON SUFFICIENT OPTIMALITY THEOREMS FOR NONSMOOTH MULTIOBJECTIVE OPTIMIZATION PROBLEMS

  • Kim, Moon-Hee;Lee, Gue-Myung
    • 대한수학회논문집
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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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MIXED TYPE DUALITY FOR CONTROL PROBLEMS WITH GENERALIZED INVEXITY

  • Husain, I.;Ahmed, A.;Ahmad, B.
    • Journal of applied mathematics & informatics
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    • v.26 no.5_6
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    • pp.819-837
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    • 2008
  • A mixed type dual to the control problem in order to unify Wolfe and Mond-Weir type dual control problem is presented in various duality results are validated and the generalized invexity assumptions. It is pointed out that our results can be extended to the control problems with free boundary conditions. The duality results for nonlinear programming problems already existing in the literature are deduced as special cases of our results.

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OPTIMALITY CONDITIONS AND DUALITY RESULTS OF THE NONLINEAR PROGRAMMING PROBLEMS UNDER ρ-(p, r)-INVEXITY ON DIFFERENTIABLE MANIFOLDS

  • Jana, Shreyasi;Nahak, Chandal
    • Journal of applied mathematics & informatics
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    • v.32 no.3_4
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    • pp.491-502
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    • 2014
  • In this paper, by using the notion of ${\rho}$-(p,r)-invexity assumptions on the functions involved, optimality conditions and duality results (Mond-Weir, Wolfe and mixed type) are established on differentiable manifolds. Counterexample is constructed to justify that our investigations are more general than the existing work available in the literature.