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Analysis on a Superlinearly Convergent Augmented Lagrangian Method

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Acta Mathematica Sinica,English Series 2014年第1期30卷 1-10页

作者： ya xiang yuan State Key Laboratory of Scientific/Engineering Computing Institute of Computational Mathematics and Scientific/Engineering ComputingAcademy of Mathematics and Systems ScienceChinese Academy of Sciences

The augmented Lagrangian method is a classical method for solving constrained ***,the augmented Lagrangian method attracts much attention due to its applications to sparse optimization in compressive sensing and low rank matrix optimization ***,most Lagrangian methods use first order information to update the Lagrange multipliers,which lead to only linear *** this paper,we study an update technique based on second order information and prove that superlinear convergence can be *** properties of the update formula are given and some implementation issues regarding the new update are also discussed.

关键词： Nonlinearly constrained optimization augmented Lagrange function Lagrange multiplier convergence

A Derivative-Free Optimization Algorithm Combining Line-Search and Trust-Region Techniques

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Chinese Annals of Mathematics,Series B 2023年第5期44卷 719-734页

作者： Pengcheng XIE ya-xiang yuan State Key Laboratory of Scientific/Engineering Computing Institute of Computational Mathematicsand Scientific/Engineering ComputingAcademy of Mathematics and Systems ScienceChinese Academy of SciencesUniversity of Chinese Academy of SciencesBeijing 100190China

The speeding-up and slowing-down(SUSD)direction is a novel direction,which is proved to converge to the gradient descent direction under some *** authors propose the derivative-free optimization algorithm SUSD-TR,which combines the SUSD direction based on the covariance matrix of interpolation points and the solution of the trust-region subproblem of the interpolation model function at the current iteration *** analyze the optimization dynamics and convergence of the algorithm *** of the trial step and structure step are *** results show their algorithm’s efficiency,and the comparison indicates that SUSD-TR greatly improves the method’s performance based on the method that only goes along the SUSD *** algorithm is competitive with state-of-the-art mathematical derivative-free optimization algorithms.

关键词： Nonlinear optimization Derivative-Free Quadratic model Line-Search Trust-Region

STOCHASTIC TRUST-REGION METHODS WITH TRUST-REGION RADIUS DEPENDING ON PROBABILISTIC MODELS

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Journal of Computational Mathematics 2022年第2期40卷 294-334页

作者： Xiaoyu Wang ya-xiang yuan Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems ScienceChinese Academy of SciencesBeijing 100190China University of Chinese Academy of Sciences Beijing 100049China State Key Laboratory of Scientific/Engineering Computing Institute of Computational Mathematics and Scientific/Engineering ComputingAcademy of Mathematics and Systems ScienceChinese Academy of SciencesBeijing 100190China

We present a stochastic trust-region model-based framework in which its radius is related to the probabilistic ***,we propose a specific algorithm termed STRME,in which the trust-region radius depends linearly on the gradient used to define the latest *** complexity results of the STRME method in nonconvex,convex and strongly convex settings are presented,which match those of the existing algorithms based on probabilistic *** addition,several numerical experiments are carried out to reveal the benefits of the proposed methods compared to the existing stochastic trust-region methods and other relevant stochastic gradient methods.

关键词： Trust-region methods,Stochastic optimization Probabilistic models Trust-region radius Global convergence

A ROBUST TRUST REGION ALGORITHM FOR SOLVING GENERAL NONLINEAR PROGRAMMING

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Journal of Computational Mathematics 2001年第3期19卷 309-322页

作者： Xin-wei Liu ya-xiang yuan State Key Laboratory of Scientific and Engineering Computing Institute of Computational Mathematics and Scientific/Engineering ComputingAcademy of Mathematics and Systems SciencesChinese Academy of SciencesBeijing 100080China Faculty of Science and Arts Hebei University of TechnologyTianjin 300130China

Provides information on a study which presented a trust region approach for solving nonlinear constrained optimization. Algorithm of the trust region approach; Information on the global convergence of the algorithm; N... 详细信息

关键词： trust region algorithm nonlinear programming

COMPUTE A CELIS-DENNIS-TAPIA STEP

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Journal of Computational Mathematics 2005年第5期23卷 463-478页

作者： Gai-di Li ya-xiang yuan College of Applied Sciences Beijing University of Technology Beijing 100022China LSEC ICMSECAcademy of Mathematics and System SciencesChinese Academy of Sciences Beijing 100080China

In this paper, we present an algorithm for the CDT subproblem. This problem stems from computing a trust region step of an algorithm, which was first proposed by Celis, Dennis and Tapia for equality constrained optimization. Our algorithm considers general case of the CDT subproblem, convergence of the algorithm is proved. Numerical examples are also provided.

关键词： The CDT subproblem Local solution Global solution Dual function

DISTURBED SPARSE LINEAR EQUATIONS OVER THE 0-1 FINITE FIELD

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Journal of Computational Mathematics 2006年第3期24卷 357-364页

作者： ya-xiang yuan Zhen-zhen Zheng LSEC ICMSEC Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing 100080 China

In this paper, disturbed sparse linear equations over the 0-1 finite field are considered. Due to the special structure of the problem, the standard alternating coordinate method can be implemented in such a way to yield a fast and efficient algorithm. Our alternating coordinate algorithm makes use of the sparsity of the coefficient matrix and the current residuals of the equations. Some hybrid techniques such as random restarts and genetic crossovers are also applied to improve our algorithm.

关键词： Sparse linear equation 0-1 finite field Alternating direction method Random restart Genetic hybrids.

ON MAXIMA OF DUAL FUNCTION OF THE CDT SUBPROBLEM

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Journal of Computational Mathematics 2001年第2期19卷 113-124页

作者： Xiong-da Chen ya-xiang yuan Reserach Development Center of Parallel Software Institute of SoftwareBeijing 100080China State Key Laboratory of Scientific and Engineering Computing Institute of Computational Mathematics and Ssientific/Engineering ComputingAcademy of Mathematics and Systems SciencesChinese Academy of SciencesBeijing 100080China

Focuses on a study which determined the geometry meaning of the maxima of the CDT mathematical subproblem's dual function. Properties of trust region subproblem; Approximation of the CDT feasible region; Relations bet... 详细信息

关键词： trust region subproblem global minimizer approximation

A Partial First-Order Affine-Scaling Method

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Acta Mathematica Sinica,English Series 2019年第1期35卷 1-16页

作者： Ran GU ya xiang yuan Academy of Mathematics and Systems Science Chinese Academy of Sciences

We present a partial first-order affine-scaling method for solving smooth optimization with linear inequality constraints. At each iteration, the algorithm considers a subset of the constraints to reduce the complexity. We prove the global convergence of the algorithm for general smooth objective functions, and show it converges at sublinear rate when the objective function is quadratic. Numerical experiments indicate that our algorithm is efficient.

关键词： Linear inequality constraints affine scaling interior point

Metrically regular mappings and its application to convergence analysis of a confined Newton-type method for nonsmooth generalized equations

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Science China Mathematics 2020年第1期63卷 39-60页

作者： Mohammed Harunor Rashid ya-xiang yuan Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems ScienceChinese Academy of SciencesBeijing 100190China Department of Mathematics Faculty of ScienceUniversity of Rajshahi 6205Bangladesh

Notion of metrically regular property and certain types of point-based approximations are used for solving the nonsmooth generalized equation f(x)+F(x)?0,where X and Y are Banach spaces,and U is an open subset of X,f:U→Y is a nonsmooth function and F:X■Y is a set-valued mapping with closed *** introduce a confined Newton-type method for solving the above nonsmooth generalized equation and analyze the semilocal and local convergence of this ***,under the point-based approximation of f on U and metrically regular property of f+F,we present quadratic rate of convergence of this ***,superlinear rate of convergence of this method is provided under the conditions that f admits p-point-based approximation on U and f+F is metrically *** example of nonsmooth functions that have p-point-based approximation is ***,a numerical experiment is given which illustrates the theoretical result.

关键词： set-valued mappings generalized equations metrically regular mapping semilocal convergence point-based approximation