Solving Nonlinear Complementarity Problem by a Smoothing Homotopy Method

Fan, Xiaona; Xu, Tingting; Gao, Furong

doi:10.11650/tjm.19.2015.3357

Cited by 5 publications

(5 citation statements)

References 16 publications

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“…Now differentiating 3.24 with respect to s we obtain the following system of ordinary differential equations with given initial values [7] H ′ (v(s), µ(s))…”

Section: Subcase (I) Limmentioning

confidence: 99%

Solution of Tensor Complementarity Problem Using Homotopy Function

Dutta¹,

Kumar²,

Deepmala³

et al. 2022

Preprint

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The paper aims to propose a suitable method in finding the solution of tensor complementarity problem. The tensor complementarity problem is a subclass of nonlinear complementarity problems for which the involved function is defined by a tensor. We propose a new homotopy function with smooth and bounded homotopy path to obtain solution of the tensor complementarity problem under some conditions. A homotopy continuation method is developed based on the proposed homotopy function. Several numerical examples are provided to show the effectiveness of the proposed homotopy continuation method.

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“…Now differentiating 3.24 with respect to s we obtain the following system of ordinary differential equations with given initial values [7] H ′ (v(s), µ(s))…”

Section: Subcase (I) Limmentioning

confidence: 99%

Solution of Tensor Complementarity Problem Using Homotopy Function

Dutta¹,

Kumar²,

Deepmala³

et al. 2022

Preprint

View full text Add to dashboard Cite

show abstract

“…We parameterize the homotopy path Γ (0) y with respect to s in the following form and the y-component of (y(s), λ(s)) gives the solution of LCP(q, A) for λ(s) = 0. For details, see [6]. Note that the parameter λ is updated from the Moore-Penrose inverse of the Jacobian matrix for tracing the homotopy path.…”

Section: H(y Ymentioning

confidence: 99%

Bounded Homotopy Path Approach to Find the Solution of Linear Complementarity Problems

Dutta¹,

Jana²,

Das³

2021

Preprint

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In this article, we introduce a new homotopy function to trace the trajectory by applying modified homotopy continuation method for finding the solution of the Linear Complementarity Problem. Earlier several authors attempted to propose homotopy functions based on original problems. We propose the homotopy function based on the Karush-Kuhn-Tucker condition of the corresponding quadratic programming problem of the original problem. The proposed approach extends the processability of the larger class of linear complementarity problems and overcomes the limitations of other existing homotopy approaches. We show that the homotopy path approaching the solution is smooth and bounded. We find the positive tangent direction of the homotopy path. The difficulty of finding a strictly feasible initial point for the interior point algorithm can be replaced appropriately by combining the interior point with the homotopy method. Various classes of numerical examples are illustrated to show the effectiveness of the proposed algorithm.

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“…Note that, if |T| � +∞, Lemma 1 implies that g μ k (x k ) � 0. Moreover, by the mechanism of updating μ k (10), we have μ k+1 � θμ k . en, we get the first-order global convergence of our Algorithm 1 lim k∈T (‖g μ k (x k )‖ + μ k ) � 0, i.e., Algorithm 1 can be terminated with finite steps.…”

Section: Theorem 1 Suppose That A1 and A2 Hold And Thatmentioning

confidence: 99%

“…Example 1. (Kojima-Shindo nonlinear complementarity test problem) (i) Degenerate example [7,10,11,27,38,39]:…”

Section: Numerical Experimentsmentioning

confidence: 99%

“…e traditional approach for NCP involves reformulating the problem as an optimization problem [1][2][3][4][5][6][7][8][9][10][11][12] or a nonlinear differentiable function [13][14][15][16][17][18]. In this paper, a new method for solving this optimization problem is based on the class of trust-region methods and also filter methods introduced by Fletcher and Leyffer in 1997 and subsequently published as [19].…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Convergence Analysis of a Trust-Region Multidimensional Filter Method for Nonlinear Complementarity Problems

Cao

Wang

2020

Mathematical Problems in Engineering

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For solving nonlinear complementarity problems, a new algorithm is proposed by using multidimensional filter techniques and a trust-region method. The algorithm is shown to be globally convergent under the reasonable assumptions and does not depend on any extra restoration procedure. In particular, it shows that the subproblem is a convex quadratic programming problem, which is easier to be solved. The results of numerical experiments show its efficiency.

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Solving Nonlinear Complementarity Problem by a Smoothing Homotopy Method

Cited by 5 publications

References 16 publications

Solution of Tensor Complementarity Problem Using Homotopy Function

Solution of Tensor Complementarity Problem Using Homotopy Function

Bounded Homotopy Path Approach to Find the Solution of Linear Complementarity Problems

Convergence Analysis of a Trust-Region Multidimensional Filter Method for Nonlinear Complementarity Problems

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