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A note on absolute value equations   总被引:3,自引:0,他引:3  
In this note, we reformulate a system of absolute value equations (AVEs) as a standard linear complementarity problem (LCP) without any assumption. Utilizing some known results for the LCP, existence and convexity results for the solution set of the AVE are proposed.  相似文献
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Convergence of a non-interior continuation algorithm for the monotone SCCP   总被引:1,自引:0,他引:1  
It is well known that the symmetric cone complementarity problem(SCCP) is a broad class of optimization problems which contains many optimization problems as special cases.Based on a general smoothing function,we propose in this paper a non-interior continuation algorithm for solving the monotone SCCP.The proposed algorithm solves at most one system of linear equations at each iteration.By using the theory of Euclidean Jordan algebras,we show that the algorithm is globally linearly and locally quadratically convergent under suitable assumptions.  相似文献
4.
A smoothing-type algorithm for solving system of inequalities   总被引:1,自引:0,他引:1  
In this paper we consider system of inequalities. By constructing a new smoothing function, the problem is approximated via a family of parameterized smooth equations. A Newton-type algorithm is applied to solve iteratively the smooth equations so that a solution of the problem concerned is found. We show that the algorithm is globally and locally quadratically convergent under suitable assumptions. Preliminary numerical results are reported.  相似文献
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Smoothing algorithms for complementarity problems over symmetric cones   总被引:1,自引:0,他引:1  
There recently has been much interest in studying optimization problems over symmetric cones. In this paper, we first investigate a smoothing function in the context of symmetric cones and show that it is coercive under suitable assumptions. We then extend two generic frameworks of smoothing algorithms to solve the complementarity problems over symmetric cones, and prove the proposed algorithms are globally convergent under suitable assumptions. We also give a specific smoothing Newton algorithm which is globally and locally quadratically convergent under suitable assumptions. The theory of Euclidean Jordan algebras is a basic tool which is extensively used in our analysis. Preliminary numerical results for second-order cone complementarity problems are reported.  相似文献
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By using a smooth entropy function to approximate the non-smooth max-type function, a vertical linear complementarity problem (VLCP) can be treated as a family of parameterized smooth equations. A Newton-type method with a testing procedure is proposed to solve such a system. We show that under some milder than usual assumptions the proposed algorithm finds an exact solution of VLCP in a finite number of iterations. Some computational results are included to illustrate the potential of this approach. This author’s work was partially supported by the National Natural Science Foundation of China (Grant Nos. 10271002 and 10401038). This author’s work was partially supported by the Scientific Research Foundation of Tianjin University for the Returned Overseas Chinese Scholars and the Scientific Research Foundation of Liu Hui Center for Applied Mathematics, Nankai University-Tianjin University.  相似文献
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Given , the linear complementarity problem (LCP) is to find such that (x, s) 0,s=Mx+q,xTs=0. By using the Chen-Harker-Kanzow-Smale (CHKS) smoothing function, the LCP is reformulated as a system of parameterized smooth-nonsmooth equations. As a result, a smoothing Newton algorithm, which is a modified version of the Qi-Sun-Zhou algorithm [Mathematical Programming, Vol. 87, 2000, pp. 1–35], is proposed to solve the LCP with M being assumed to be a P0-matrix (P0–LCP). The proposed algorithm needs only to solve one system of linear equations and to do one line search at each iteration. It is proved in this paper that the proposed algorithm has the following convergence properties: (i) it is well-defined and any accumulation point of the iteration sequence is a solution of the P0–LCP; (ii) it generates a bounded sequence if the P0–LCP has a nonempty and bounded solution set; (iii) if an accumulation point of the iteration sequence satisfies a nonsingularity condition, which implies the P0–LCP has a unique solution, then the whole iteration sequence converges to this accumulation point sub-quadratically with a Q-rate 2–t, where t(0,1) is a parameter; and (iv) if M is positive semidefinite and an accumulation point of the iteration sequence satisfies a strict complementarity condition, then the whole sequence converges to the accumulation point quadratically.This authors work is supported by the Hong Kong Research Grant Council and the Australian Research Council.This authors work is supported by Grant R146-000-035-101 of National University of Singapore.Mathematics Subject Classification (1991): 90C33, 65K10  相似文献
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基于黄正海等2001年提出的光滑函数,本文给出一个求解P0函数非线性互补问题的非内部连续化算法.所给算法拥有一些好的特性.在较弱的条件下,证明了所给算法或者是全局线性收敛,或者是全局和局部超线性收敛.给出了所给算法求解两个标准测试问题的数值试验结果.  相似文献
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In this paper we propose a smoothing Newton-type algorithm for the problem of minimizing a convex quadratic function subject to finitely many convex quadratic inequality constraints. The algorithm is shown to converge globally and possess stronger local superlinear convergence. Preliminary numerical results are also reported. Mathematics Subject Classification (1991): 90C33, 65K10 This author’s work was also partially supported by the Scientific Research Foundation of Tianjin University for the Returned Overseas Chinese Scholars and the Scientific Research Foundation of Liu Hui Center for Applied Mathematics, Nankai University-Tianjin University.  相似文献
10.
We propose a non-interior continuation algorithm for the solution of the linear complementarity problem (LCP) with a P0 matrix. The proposed algorithm differentiates itself from the current continuation algorithms by combining good global convergence properties with good local convergence properties under unified conditions. Specifically, it is shown that the proposed algorithm is globally convergent under an assumption which may be satisfied even if the solution set of the LCP is unbounded. Moreover, the algorithm is globally linearly and locally superlinearly convergent under a nonsingularity assumption. If the matrix in the LCP is a P* matrix, then the above results can be strengthened to include global linear and local quadratic convergence under a strict complementary condition without the nonsingularity assumption.  相似文献
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