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On the direct searches for non-smooth stochastic optimization problems

Journal of Systems Engineering and Electronics 2009年第4期20卷 889-898页

作者： Huang Tianyun School of Computer Science and Technology Southwest Univ. for Nationalities Chengdu 510041 P. R. China

Many difficult engineering problems cannot be solved by the conventional optimization techniques in practice. Direct searches that need no recourse to explicit derivatives are revived and become popular since the new century. In order to get a deep insight into this field, some notes on the direct searches for non-smooth optimization problems are made. The global convergence vs. local convergence and their influences on expected solutions for simulation-based stochastic optimization are pointed out. The sufficient and simple decrease criteria for step acceptance are analyzed, and why simple decrease is enough for globalization in direct searches is identified. The reason to introduce the positive spanning set and its usage in direct searches is explained. Other topics such as the generalization of direct searches to bound, linear and non-linear constraints are also briefly discussed.

关键词： non-linear programming non-smooth optimization stochastic simulation direct searches positive spanning set convergence analysis pattern selection.

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求解一类非光滑优化问题的改进变尺度方法

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高等学校计算数学学报 2006年第1期28卷 20-25页

作者：程浩刘国庆南京工业大学理学院南京工业大学理学院南京 210009

This paper describes a methodology to derive algorithms for non-smooth optimization. The algorithm development methodology uses slack variables and weighting coefficients for the inequality constraints and a factored representation for the gradient. The algorithm has two integral parts: a feasible initial estimate of the real signal and the iteration process that deduces the best basis selection. The iterations are based on weighted minimization of the dependent variables with the weights being sufficient small. The result of global convergence and the rate of global convergence are presented. Performance of the algorithm is illustrated on computer simulations.

关键词： non-smooth optimization affine scaling transformation global convergence.

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IMPLICIT DETERMINANT METHOD FOR SOLVING AN HERMITIAN EIGENVALUE optimization PROBLEM

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Journal of Computational Mathematics 2023年第6期41卷 1117-1136页

作者： Siru Gong Yangfeng Su School of Mathematical Sciences Fudan UniversityShanghai 200433China

Implicit determinant method is an effective method for some linear eigenvalue optimization problems since it solves linear systems of equations rather than *** this paper,we generalize the implicit determinant method to solve an Hermitian eigenvalue optimization problem for smooth case and non-smooth *** prove that the implicit determinant method converges locally and *** experiments confirm our theoretical results and illustrate the efficiency of implicit determinant method.

关键词： Eigenvalue optimization Multiple eigenvalue non-smooth optimization Implicit determinant method Crawford number

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An Exact Penalty Method for Constrained Distributed optimization 36

An Exact Penalty Method for Constrained Distributed Optimiza...

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第36届中国控制会议

作者： Hongbing Zhou Xianlin Zeng Yiguang Hong Key Laboratory of Systems and Control Institute of Systems ScienceChinese Academy of Sciences

ISBN: (纸本)9781538629185

This paper focuses on a distributed non-smooth constrained optimization problem,in which the non-smoothness means the continuity but *** optimization deals with optimizing a sum of objective functions,each function is known by one agent due to many reasons such as privacy and *** all the agent reach an global optimal by communicating through an interaction *** proposed an exact penalty algorithm for constrained distributed optimization,which has some good properties when we design a continuous-time *** we rigorously prove the efficiency of this *** also put a numerical example to show the efficacy of the proposed algorithm.

关键词： Exact penalty method distributed algorithm non-smooth optimization continuous-time multi-agent systems

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Convergence analysis of an infeasible quasi- Newton bundle method for nonsmooth convex programming

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Frontiers of Mathematics in China 2023年第5期18卷 367-380页

作者： Jie SHEN Fangfang GUO Liping PANG School of Mathematics Liaoning Normal UniversityDalian 116029China School of Mathematical Sciences Dalian University of TechnologyDalian 116024China

By utilizing the improvement function,we change the nonsmooth convex constrained optimization into an unconstrained optimization,and construct an infeasible quasi-Newton bundle method with proximal *** should be noted that the objective function being minimized in unconstrained optimization subproblem may vary along the iterations(it does not change if the null step is made,otherwise it is updated to a new function).It is necessary to make some adjustment in order to obtain the convergence *** employ the main idea of infeasible bundle method of Sagastizabal and Solodov,and under the circumstances that each iteration point may be infeasible for primal problem,we prove that each cluster point of the sequence generated by the proposed algorithm is the optimal solution to the original ***,for BFGS quasi-Newton algorithm with strong convex objective function,we obtain the condition which guarantees the boundedness of quasi-Newton matrices and the R-linear convergence of the iteration points.

关键词： non-smooth optimization convex constraint improvement function bundle method quasi-Newton direction

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Almost Sure Convergence of Proximal Stochastic Accelerated Gradient Methods

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Journal of Applied Mathematics and Physics 2024年第4期12卷 1321-1336页

作者： Xin Xiang Haoming Xia Key Laboratory of optimization Theory and Applications School of Mathematics and Information China West Normal University Nanchong China

Proximal gradient descent and its accelerated version are resultful methods for solving the sum of smooth and non-smooth problems. When the smooth function can be represented as a sum of multiple functions, the stochastic proximal gradient method performs well. However, research on its accelerated version remains unclear. This paper proposes a proximal stochastic accelerated gradient (PSAG) method to address problems involving a combination of smooth and non-smooth components, where the smooth part corresponds to the average of multiple block sums. Simultaneously, most of convergence analyses hold in expectation. To this end, under some mind conditions, we present an almost sure convergence of unbiased gradient estimation in the non-smooth setting. Moreover, we establish that the minimum of the squared gradient mapping norm arbitrarily converges to zero with probability one.

关键词： Proximal Stochastic Accelerated Method Almost Sure Convergence Composite optimization non-smooth optimization Stochastic optimization Accelerated Gradient Method

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Modeling the Berth Allocation Problem in Container Terminals

Modeling the Berth Allocation Problem in Container Terminals

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第二十九届中国控制会议

作者： JIN Li1,YU Hongxia2,3 1.School of Mathematics,Physics and Information Science,Zhejiang Ocean University,Zhoushan 316004,P.R.China2.Antai College of Economics&Management,Shanghai JiaoTong University,Shanghai 200052,P.R.China 3.Department of Mathematics and physics,Shanghai University of Electric Power,Shanghai 200090,P.R.China

Berth Allocation problems are usually studied by using bin-packing method,integer programming method and simu-lation *** this paper,non-smooth optimization and nonlinear programming approaches are used to formulate the Berth Allocation problem as a general optimization *** general model is given a nonlinear programming representation and the first-order optimality conditions.

关键词： Container Terminals Berth Allocation non-smooth optimization

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有可再生能源和电力存储设施并网的智能电网优化用电策略

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管理科学 2019年第6期

作者：陶莉高岩朱红波曹磊

大量可再生能源和存储设施集中或分布接入电网，缓解了电网的供给压力，但同时也对电力系统安全造成新的威胁。合理使用新能源和可存储设施使之更好为电网服务，是现代电网亟待解决的一个问题。本文对有可存储设备和可再生能源并网的电... 详细信息

大量可再生能源和存储设施集中或分布接入电网，缓解了电网的供给压力，但同时也对电力系统安全造成新的威胁。合理使用新能源和可存储设施使之更好为电网服务，是现代电网亟待解决的一个问题。本文对有可存储设备和可再生能源并网的电力系统进行研究，根据可再生能源在实际生活中的情形，将其划分为两类：私人新能源发电和公共新能源发电，其中私人新能源发电可供自身直接使用，多余部分并入电网，而公共新能源发电直接并入电网，然后针对上述复杂情形，结合用户实际需求，以所有用户效用最大化、成本最小化为目标函数，建立优化模型，给出了一种既有可存储设备又有可再生能源复杂并网情况下用户优化用电策略——包括家用电器、新能源、以及存储设备充放电策略。对模型的性质进行研究，考虑到模型是凸规划，强对偶成立，用拉格朗日对偶算法给出了模型的解。求解过程中，由于目标函数是非光滑的，采用光滑化的技术将目标函数光滑化，将非光滑问题转化为光滑问题，进一步利用拟牛顿下降法求解。该策略能确保新能源得到优先、充分利用，体现用户效用最大化、成本最小化，同时可以避免由于新能源并网可能会造成电网不稳定情况的出现；光滑化的方法不但适用于本文，经过适当改进后也可适用于其他目标函数为非光滑的情况。仿真结果验证了模型的合理性和算法的可行性。

关键词：智能电网需求侧管理可再生能源电力存储设施拉格朗日对偶方法非光滑优化拟牛顿法 smart grid demand side management renewable energy storage device Lagrangian dual method non-smooth optimization Quasi-Newton method

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