Journal Article10.1007/BF00934289
An iterative method for generalized nonlinear complementarity problems
G. J. Habetler,A. L. Price +1 more
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TL;DR: In this article, an iterative method for solving generalized nonlinear complementarity problems involving stronglyK-copositive operators is introduced, conditions are presented which guarantee the convergence of the method; in addition, the sequence of iterates is used to prove the existence of a solution to the problem under conditions not included in the previous study.
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Abstract: An iterative method for solving generalized nonlinear complementarity problems (Ref. 1) involving stronglyK-copositive operators is introduced. Conditions are presented which guarantee the convergence of the method; in addition, the sequence of iterates is used to prove the existence of a solution to the problem under conditions not included in the previous study. Separate consideration is given to the generalized linear complementarity problem.
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Citations
An iterative method for generalized complementarity problems
TL;DR: In this paper, the generalized complementarity problem is solved under the condition that the function is Lipschitz continuous and strongly monotone on the (possibly nonsolid) cone.
39
Nonlinear quasi complementarity problems
TL;DR: In this paper, an iterative algorithm is given to obtain the approximate solution of a new class of complementarity problems, and it is shown that the approximation solution obtained by the iterative scheme converges to the exact solution.
23
Convergence analysis of the iterative methods for quasi-complementarity problems.
TL;DR: The iterative methods for the quasi complementarity problems of the formu−m(u)≥0, T(u),T(u))=0, where m is a point-to-point mapping and T is a continuous mapping from Rn into itself is considered.
Three classes of merit functions for the complementarity problem over a closed convex cone
Nan Lu,Zheng-Hai Huang +1 more
TL;DR: In this article, the authors considered the complementarity problem over a closed convex cone in a Hilbert space, and proposed three classes of merit functions for solving such a problem, including natural residual merit functions, LT merit functions and implicit Lagrangian merit functions.
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References
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Positive solutions of operator equations
A. R. Brodsky,M. A. Krasnosel'skii,Richard E. Flaherty,Leo F. Boron +3 more
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The Generalized Complementarity Problem.
S. Karamardian
- 01 Aug 1970
TL;DR: In this paper, a general complementarity problem (GCP) is defined, where the setting is a locally convex Hausdorff topological vector space X, the nonnegative orthant is replaced by a convex closed cone K in X, and the usual non-negative partial ordering is induced by the cone K and its polar cone K*.
286
The nonlinear complementarity problem with applications, part 2
TL;DR: The main existence and uniqueness theorem of Part 1 is applied to three specific problems, namely, (a) the symmetric, dual, nonlinear programs of Dantzig, Eisenberg, and Cottle, (b) the saddle point problem of a differentiable scalar function over an unbounded product set, and (c) the equilibrium-point problem of ann-person game as mentioned in this paper.
117
Existence theory for generalized nonlinear complementarity problems
G. J. Habetler,A. L. Price +1 more
TL;DR: In this article, the nonlinear complementarity problem is generalized by replacing the usual nonnegative ordering of Rn by an ordering generated by a convex cone, which is used to guarantee the existence of a solution to the generalized problem.