• Title/Summary/Keyword: nondifferentiable programming

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ON SYMMETRIC DUALITY IN NONDIFFERENTIABLE MATHEMATICAL PROGRAMMING WITH F-CONVEXITY

  • AHMAD I.;HUSAIN Z.
    • Journal of applied mathematics & informatics
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    • v.19 no.1_2
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    • pp.371-384
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    • 2005
  • Usual symmetric duality results are proved for Wolfe and Mond-Weir type nondifferentiable nonlinear symmetric dual programs under F-convexity F-concavity and F-pseudoconvexity F-pseudoconcavity assumptions. These duality results are then used to formulate Wolfe and Mond-Weir type nondifferentiable minimax mixed integer dual programs and symmetric duality theorems are established. Moreover, nondifferentiable fractional symmetric dual programs are studied by using the above programs.

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.

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.

MULTIOBJECTIVE CONTINUOUS PROGRAMMING CONTAINING SUPPORT FUNCTIONS

  • Husain, I.;Ahmed, A.;Rumana, G. Mattoo
    • Journal of applied mathematics & informatics
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    • v.27 no.3_4
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    • pp.603-619
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    • 2009
  • Wolfe and Mond-Weir type dual to a nondifferentiable continuous programming containing support functions are formulated and duality is investigated for these two dual models under invexity and generalized invexity. A close relationship of our duality results with those of nondifferentiable nonlinear programming problem is also pointed out.

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NONDIFFERENTIABLE SECOND-ORDER MINIMAX MIXED INTEGER SYMMETRIC DUALITY

  • Gulati, Tilak Raj;Gupta, Shiv Kumar
    • Journal of the Korean Mathematical Society
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    • v.48 no.1
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    • pp.13-21
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    • 2011
  • In this paper, a pair of Wolfe type nondifferentiable sec-ond order symmetric minimax mixed integer dual problems is formu-lated. Symmetric and self-duality theorems are established under $\eta_1$-bonvexity/$\eta_2$-boncavity assumptions. Several known results are obtained as special cases. Examples of such primal and dual problems are also given.

OPTIMALITY AND DUALITY IN NONDIFFERENTIABLE MULTIOBJECTIVE FRACTIONAL PROGRAMMING USING α-UNIVEXITY

  • Gupta, Rekha;Srivastava, Manjari
    • Journal of applied mathematics & informatics
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    • v.32 no.3_4
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    • pp.359-375
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    • 2014
  • In this paper, a multiobjective nondifferentiable fractional programming problem (MFP) is considered where the objective function contains a term involving the support function of a compact convex set. A vector valued (generalized) ${\alpha}$-univex function is defined to extend the concept of a real valued (generalized) ${\alpha}$-univex function. Using these functions, sufficient optimality criteria are obtained for a feasible solution of (MFP) to be an efficient or weakly efficient solution of (MFP). Duality results are obtained for a Mond-Weir type dual under (generalized) ${\alpha}$-univexity assumptions.

ON OPTIMALITY AND DUALITY FOR GENERALIZED NONDIFFERENTIABLE FRACTIONAL OPTIMIZATION PROBLEMS

  • Kim, Moon-Hee;Kim, Gwi-Soo
    • Communications of the Korean Mathematical Society
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    • v.25 no.1
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    • pp.139-147
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    • 2010
  • A generalized nondifferentiable fractional optimization problem (GFP), which consists of a maximum objective function defined by finite fractional functions with differentiable functions and support functions, and a constraint set defined by differentiable functions, is considered. Recently, Kim et al. [Journal of Optimization Theory and Applications 129 (2006), no. 1, 131-146] proved optimality theorems and duality theorems for a nondifferentiable multiobjective fractional programming problem (MFP), which consists of a vector-valued function whose components are fractional functions with differentiable functions and support functions, and a constraint set defined by differentiable functions. In fact if $\overline{x}$ is a solution of (GFP), then $\overline{x}$ is a weakly efficient solution of (MFP), but the converse may not be true. So, it seems to be not trivial that we apply the approach of Kim et al. to (GFP). However, modifying their approach, we obtain optimality conditions and duality results for (GFP).

MULTIOBJECTIVE SECOND-ORDER NONDIFFERENTIABLE SYMMETRIC DUALITY INVOLVING (F, $\alpha$, $\rho$, d)-CONVEX FUNCTIONS

  • Gupta, S.K.;Kailey, N.;Sharma, M.K.
    • Journal of applied mathematics & informatics
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    • v.28 no.5_6
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    • pp.1395-1408
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    • 2010
  • In this paper, a pair of Wolfe type second-order nondifferentiable multiobjective symmetric dual program over arbitrary cones is formulated. Weak, strong and converse duality theorems are established under second-order (F, $\alpha$, $\rho$, d)-convexity assumptions. An illustration is given to show that second-order (F, $\alpha$, $\rho$, d)-convex functions are generalization of second-order F-convex functions. Several known results including many recent works are obtained as special cases.

An algorithm for computer-aided controller design using semi-infinite programming technique (SIP를 이용한 computer-aided 제어기 설계에 대한 알고리즘)

  • 권태용;이종용;이상효
    • 제어로봇시스템학회:학술대회논문집
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    • 1986.10a
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    • pp.629-632
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    • 1986
  • Both combinatorial and parametric optimization are used in computer-aided design(CAD). The most commonly occuring parametric optimization problems in engineering design such as design of control systems, design of electric circuits are usually expressed either as differentiable or as nondifferentiable semi-infinite programming(SIP) problems. In this paper we express algorithms for a class of computer-aided design problems arising in control systems.

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