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A TRULY GLOBALLY CONVERGENT FEASIBLE newton-type METHOD FOR MIXED COMPLEMENTARITY PROBLEMS

Journal of Computational Mathematics 2004年第3期22卷 347-360页

作者： DerenHan SchoolofMathematicsandComputerScience NanjingNormalUniversityNanjing210097China

Typical solution methods for solving mixed complementarity problems either generate feasible iterates but have to solve relatively complicated subproblems such as quadratic programs or linear complementarity problems, or (those methods) have relatively simple subproblems such as system of linear equations but possibly generate infeasible *** this paper, we propose a new newton-type method for solving monotone mixed complementarity problems, which ensures to generate feasible iterates, and only has to solve a system of well-conditioned linear equations with reduced dimension per iteration. Without any regularity assumption, we prove that the whole sequence of iterates converges to a solution of the problem (truly globally convergent). Furthermore, under suitable conditions,the local superlinear rate of convergence is also established.

关键词： Global convergence Mixed complementarity problems newton-type methods Superlinear convergence.

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newton-type Optimal Thresholding Algorithms for Sparse Optimization Problems

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Journal of the Operations Research Society of China 2022年第3期10卷 447-469页

作者： Nan Meng Yun-Bin Zhao School of Mathematics University of BirminghamEdgbastonBirmingham B152TTUK Shenzhen Research Institute of Big Data Chinese University of Hong KongShenzhen 518172GuangdongChina

Sparse signals can be possibly reconstructed by an algorithm which merges a traditional nonlinear optimization method and a certain thresholding *** from existing thresholding methods,a novel thresholding technique referred to as the optimal k-thresholding was recently proposed by Zhao(SIAM J Optim 30(1):31-55,2020).This technique simultaneously performs the minimization of an error metric for the problem and thresholding of the iterates generated by the classic gradient *** this paper,we propose the so-called newton-type optimal k-thresholding(NTOT)algorithm which is motivated by the appreciable performance of both newton-type methods and the optimal k-thresholding technique for signal *** guaranteed performance(including convergence)of the proposed algorithms is shown in terms of suitable choices of the algorithmic parameters and the restricted isometry property(RIP)of the sensing matrix which has been widely used in the analysis of compressive sensing *** simulation results based on synthetic signals indicate that the proposed algorithms are stable and efficient for signal recovery.

关键词： Compressed sensing Sparse optimization newton-type methods Optimal k-thresholding Restricted isometry property

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