• Title, Summary, Keyword: Symmetric duality

Search Result 14, Processing Time 0.044 seconds

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

  • Kim, Do-Sang;Song, Young-Ran
    • Journal of the Korean Mathematical Society
    • /
    • v.37 no.6
    • /
    • pp.1021-1030
    • /
    • 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.

  • PDF

SYMMETRIC DUALITY FOR A CLASS OF NONDIFFERENTIABLE VARIATIONAL PROBLEMS WITH INVEXITY

  • LEE, WON JUNG
    • Journal of the Korean Society for Industrial and Applied Mathematics
    • /
    • v.6 no.1
    • /
    • pp.67-80
    • /
    • 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.

  • PDF

MULTIOBJECTIVE FRACTIONAL SYMMETRIC DUALITY INVOLVING CONES

  • Ahmad, I.;Sharma, Sarita
    • Journal of applied mathematics & informatics
    • /
    • v.26 no.1_2
    • /
    • pp.151-160
    • /
    • 2008
  • A pair of multiobjective fractional symmetric dual programs is formulated over arbitrary cones. Weak, strong and converse duality theorems are proved under pseudoinvexity assumptions. A self duality theorem is also discussed.

  • PDF

NONDIFFERENTIABLE SECOND-ORDER MINIMAX MIXED INTEGER SYMMETRIC DUALITY

  • Gulati, Tilak Raj;Gupta, Shiv Kumar
    • Journal of the Korean Mathematical Society
    • /
    • v.48 no.1
    • /
    • pp.13-21
    • /
    • 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.

NONDIFFERENTIABLE SECOND ORDER SELF AND SYMMETRIC DUAL MULTIOBJECTIVE PROGRAMS

  • Husain, I.;Ahmed, A.;Masoodi, Mashoob
    • Journal of applied mathematics & informatics
    • /
    • v.26 no.3_4
    • /
    • pp.549-561
    • /
    • 2008
  • In this paper, we construct a pair of Wolfe type second order symmetric dual problems, in which each component of the objective function contains support function and is, therefore, nondifferentiable. For this problem, we validate weak, strong and converse duality theorems under bonvexity - boncavity assumptions. A second order self duality theorem is also proved under additional appropriate conditions.

  • PDF

DISCRETE DUALITY FOR TSH-ALGEBRAS

  • Figallo, Aldo Victorio;Pelaitay, Gustavo;Sanza, Claudia
    • Communications of the Korean Mathematical Society
    • /
    • v.27 no.1
    • /
    • pp.47-56
    • /
    • 2012
  • In this article, we continue the study of tense symmetric Heyting algebras (or TSH-algebras). These algebras constitute a generalization of tense algebras. In particular, we describe a discrete duality for TSH-algebras bearing in mind the results indicated by Or lowska and Rewitzky in [E. Orlowska and I. Rewitzky, Discrete Dualities for Heyting Algebras with Operators, Fund. Inform. 81 (2007), no. 1-3, 275-295] for Heyting algebras. In addition, we introduce a propositional calculus and prove this calculus has TSH-algebras as algebraic counterpart. Finally, the duality mentioned above allowed us to show the completeness theorem for this calculus.

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
    • /
    • v.28 no.5_6
    • /
    • pp.1395-1408
    • /
    • 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.

The $\epsilon$-Symmetric Relation Between the Lagrangean Relaxation and the Benders' Decomposition for Large Scale Mixed Integer Programming (대규모 혼합전수계획 문제를 풀기 위한 라구랑지 이완기법과 벤더스 분할기법과의 대칭적 관계)

  • 조성철;김세헌
    • Journal of the Korean Operations Research and Management Science Society
    • /
    • v.14 no.2
    • /
    • pp.19-26
    • /
    • 1989
  • We in this paper have defined the concept of .epsilon.-symmetric relation between the Lagrangean relaxation and the Benders' decomposition. This links the solutions of the Lagrangean subproblems and those of the Benders' subproblems even under positive duality gaps. As an application we have discussed the reduction of the size for a special class of problems.

  • PDF