• Title/Summary/Keyword: Complementarity problems

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Algorithmic Properties of Isotone Complementarity Problems

  • Ahn, Byong-Hun
    • Journal of the Korean Operations Research and Management Science Society
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    • v.12 no.1
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    • pp.10-18
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    • 1987
  • This paper discusses algorithmic properties of a class of complementarity programs involving strictly diagonally isotone and off-diagonally isotone functions, i. e., functions whose Jacobian matrices have positive diagonal elements and nonnegative off-diagonal elements, A typical traffic equilibrium under elastic demands is cast into this class. Algorithmic properties of these complementarity problems, when a Jacobi-type iteration is applied, are investigated. It is shown that with a properly chosen starting point the generated sequence are decomposed into two converging monotonic subsequences. This and related will be useful in developing solution procedures for this class of complementarity problems.

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MERIT FUNCTIONS FOR MATRIX CONE COMPLEMENTARITY PROBLEMS

  • Wang, Li;Liu, Yong-Jin;Jiang, Yong
    • Journal of applied mathematics & informatics
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    • v.31 no.5_6
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    • pp.795-812
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    • 2013
  • The merit function arises from the development of the solution methods for the complementarity problems defined over the cone of non negative real vectors and has been well extended to the complementarity problems defined over the symmetric cones. In this paper, we focus on the extension of the merit functions including the gap function, the regularized gap function, the implicit Lagrangian and others to the complementarity problems defined over the nonsymmetric matrix cone. These theoretical results of this paper suggest new solution methods based on unconstrained and/or simply constrained methods to solve the matrix cone complementarity problems (MCCP).

A NEW CLASS OF RANDOM COMPLETELY GENERALIZED STRONGLY NONLINEAR QUASI-COMPLEMENTARITY PROBLEMS FOR RANDOM FUZZY MAPPINGS

  • Huang, Nam-Jing
    • Journal of applied mathematics & informatics
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    • v.5 no.2
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    • pp.357-372
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    • 1998
  • In this paper we introduce and study a new class of random completely generalized strongly nonlinear quasi -comple- mentarity problems with non-compact valued random fuzzy map-pings and construct some new iterative algorithms for this kind of random fuzzy quasi-complementarity problems. We also prove the existence of random solutions for this class of random fuzzy quasi-complementarity problems and the convergence of random iterative sequences generated by the algorithms.

RANDOM GENERALIZED SET-VALUED COMPLEMENTARITY PROBLEMS

  • Lee, Byung-Soo;Huang, Nan-Jing
    • Journal of the Korean Mathematical Society
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    • v.34 no.1
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    • pp.1-12
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    • 1997
  • Complementaity problem theory developed by Lemke [10], Cottle and Dantzig [8] and others in the early 1960s and thereafter, has numerous applications in diverse fields of mathematical and engineering sciences. And it is closely related to variational inquality theory and fixed point theory. Recently, fixed point methods for the solving of nonlinear complementarity problems were considered by Noor et al. [11, 12]. Also complementarity problems related to variational inequality problems were investigated by Chang [1], Cottle [7] and others.

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GENERALIZED MILDLY NONLINEAR COMPLEMENTARITY PROBLEMS FOR FUZZY MAPPINGS

  • Al Said, Elsa-A.;Noor, Muhammad-Aslam
    • Journal of applied mathematics & informatics
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    • v.5 no.3
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    • pp.659-668
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    • 1998
  • In this paper we introduce and study a new class of gen-eralized mildly nonlinear complementarity problems for fuzzy map-pings. We use the change of variabes technique to establish the equivalence between the generalized mildly nonlinear complementar-ity problems and the Wiener-Hopf equations. This equivalence is used to suggest and analyze a number of iterative algorithm for solv-ing the generalized mildly nonlinear complemetarity problems.

MIXED VECTOR FQ-IMPLICIT VARIATIONAL INEQUALITIES WITH FQ-COMPLEMENTARITY PROBLEMS

  • Lee, Byung-Soo
    • Honam Mathematical Journal
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    • v.31 no.2
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    • pp.247-258
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    • 2009
  • This paper introduces new mixed vector FQ-implicit variational inequality problems and corresponding mixed vector FQ-implicit complementarity problems for set-valued mappings, and studies the equivalence between them under certain assumptions in Banach spaces. It also derives some new existence theorems of solutions for them with examples under suitable assumptions without monotonicity. This paper generalizes and extends many results in [8, 10, 19-22].

Fuzzy-Enforced Complementarity Constraints in Nonlinear Interior Point Method-Based Optimization

  • Song, Hwachang
    • International Journal of Fuzzy Logic and Intelligent Systems
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    • v.13 no.3
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    • pp.171-177
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    • 2013
  • This paper presents a fuzzy set method to enforce complementarity constraints (CCs) in a nonlinear interior point method (NIPM)-based optimization. NIPM is a Newton-type approach to nonlinear programming problems, but it adopts log-barrier functions to deal with the obstacle of managing inequality constraints. The fuzzy-enforcement method has been implemented for CCs, which can be incorporated in optimization problems for real-world applications. In this paper, numerical simulations that apply this method to power system optimal power flow problems are included.