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A New Nonmonotonic Trust Region Algorithm for A Class of Unconstrained Nonsmooth Optimization
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作者 欧宜贵 侯定丕 《Northeastern Mathematical Journal》 CSCD 2002年第4期335-342,共8页
This paper presents a new trust region algorithm for solving a class of composite nonsmooth optimizations. It is distinguished by the fact that this method does not enforce strict monotonicity of the objective functio... This paper presents a new trust region algorithm for solving a class of composite nonsmooth optimizations. It is distinguished by the fact that this method does not enforce strict monotonicity of the objective function values at successive iterates and that this method extends the existing results for this type of nonlinear optimization with smooth, or piecewise smooth, or convex objective functions or their composition. It is proved that this algorithm is globally convergent under certain conditions. Finally, some numerical results for several optimization problems are reported which show that the nonmonotonic trust region method is competitive with the usual trust region method. 展开更多
关键词 nonmonotonic strategy trust region method composite nonsmooth optimization
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Accelerated Primal-Dual Projection Neurodynamic Approach With Time Scaling for Linear and Set Constrained Convex Optimization Problems
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作者 You Zhao Xing He +1 位作者 Mingliang Zhou Tingwen Huang 《IEEE/CAA Journal of Automatica Sinica》 SCIE EI CSCD 2024年第6期1485-1498,共14页
The Nesterov accelerated dynamical approach serves as an essential tool for addressing convex optimization problems with accelerated convergence rates.Most previous studies in this field have primarily concentrated on... The Nesterov accelerated dynamical approach serves as an essential tool for addressing convex optimization problems with accelerated convergence rates.Most previous studies in this field have primarily concentrated on unconstrained smooth con-vex optimization problems.In this paper,on the basis of primal-dual dynamical approach,Nesterov accelerated dynamical approach,projection operator and directional gradient,we present two accelerated primal-dual projection neurodynamic approaches with time scaling to address convex optimization problems with smooth and nonsmooth objective functions subject to linear and set constraints,which consist of a second-order ODE(ordinary differential equation)or differential conclusion system for the primal variables and a first-order ODE for the dual vari-ables.By satisfying specific conditions for time scaling,we demonstrate that the proposed approaches have a faster conver-gence rate.This only requires assuming convexity of the objective function.We validate the effectiveness of our proposed two accel-erated primal-dual projection neurodynamic approaches through numerical experiments. 展开更多
关键词 Accelerated projection neurodynamic approach lin-ear and set constraints projection operators smooth and nonsmooth convex optimization time scaling.
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The Convergence of the Steepest Descent Algorithm for D.C.Optimization 被引量:1
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作者 SONG Chun-ling XIA Zun-quan 《Chinese Quarterly Journal of Mathematics》 CSCD 北大核心 2007年第1期131-136,共6页
Some properties of a class of quasi-differentiable functions(the difference of two finite convex functions) are considered in this paper. And the convergence of the steepest descent algorithm for unconstrained and c... Some properties of a class of quasi-differentiable functions(the difference of two finite convex functions) are considered in this paper. And the convergence of the steepest descent algorithm for unconstrained and constrained quasi-differentiable programming is proved. 展开更多
关键词 nonsmooth optimization D. C. optimization upper semi-continuous lower semi-continuous steepest descent algorithm CONVERGENCE
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A FILTER-TRUST-REGION METHOD FOR LC^1 UNCONSTRAINED OPTIMIZATION AND ITS GLOBAL CONVERGENCE 被引量:1
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作者 ZhenghaoYang Wenyu Sun Chuangyin Dang 《Analysis in Theory and Applications》 2008年第1期55-66,共12页
In this paper we present a filter-trust-region algorithm for solving LC1 unconstrained optimization problems which uses the second Dini upper directional derivative. We establish the global convergence of the algorith... In this paper we present a filter-trust-region algorithm for solving LC1 unconstrained optimization problems which uses the second Dini upper directional derivative. We establish the global convergence of the algorithm under reasonable assumptions. 展开更多
关键词 nonsmooth optimization filter method trust region algorithm global conver- gence LC1 optimization
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NONSMOOTH MODEL FOR PLASTIC LIMIT ANALYSIS AND ITS SMOOTHING ALGORITHM
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作者 李建宇 潘少华 李兴斯 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2006年第8期1081-1088,共8页
By means of Lagrange duality of Hill's maximum plastic work principle theory of the convex program, a dual problem under Mises' yield condition has been derived and whereby a non-differentiable convex optimization m... By means of Lagrange duality of Hill's maximum plastic work principle theory of the convex program, a dual problem under Mises' yield condition has been derived and whereby a non-differentiable convex optimization model for the limit analysis is developed. With this model, it is not necessary to linearize the yield condition and its discrete form becomes a minimization problem of the sum of Euclidean norms subject to linear constraints. Aimed at resolving the non-differentiability of Euclidean norms, a smoothing algorithm for the limit analysis of perfect-plastic continuum media is proposed. Its efficiency is demonstrated by computing the limit load factor and the collapse state for some plane stress and plain strain problems. 展开更多
关键词 plastic limit analysis DUALITY nonsmooth optimization smoothing method
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Newton type methods for solving nonsmooth equations
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作者 Gao Yan 《Journal of Systems Engineering and Electronics》 SCIE EI CSCD 2005年第4期811-815,共5页
Numerical methods for the solution of nonsmooth equations are studied. A new subdifferential for a locally Lipschitzian function is proposed. Based on this subdifferential, Newton methods for solving nonsmooth equatio... Numerical methods for the solution of nonsmooth equations are studied. A new subdifferential for a locally Lipschitzian function is proposed. Based on this subdifferential, Newton methods for solving nonsmooth equations are developed and their convergence is shown. Since this subdifferential is easy to be computed, the present Newton methods can be executed easily in some applications. 展开更多
关键词 nonsmooth equations newton methods SUBDIFFERENTIAL nonsmooth optimization.
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Solving constrained minimax problem via nonsmooth equations method
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作者 郭修霞 《Journal of Coal Science & Engineering(China)》 2004年第1期109-111,共3页
A new nonsmooth equations model of constrained minimax problem was de-rived. The generalized Newton method was applied for solving this system of nonsmooth equations system. A new algorithm for solving constrained min... A new nonsmooth equations model of constrained minimax problem was de-rived. The generalized Newton method was applied for solving this system of nonsmooth equations system. A new algorithm for solving constrained minimax problem was established. The local superlinear and quadratic convergences of the algorithm were discussed. 展开更多
关键词 nonsmooth equations minimax problem generalized newton method nonsmooth optimization
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FILLED FUNCTIONS FOR UNCONSTRAINED GLOBAL OPTIMIZATION 被引量:1
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作者 XuZheng XuChengxian 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2000年第3期307-318,共12页
The paper is concerned with the filled functions for global optimization of a continuous function of several variables.More general forms of filled functions are presented for smooth and nonsmooth optimizations.These ... The paper is concerned with the filled functions for global optimization of a continuous function of several variables.More general forms of filled functions are presented for smooth and nonsmooth optimizations.These functions have either two adjustable parameters or one adjustable parameter.Conditions on functions and on the values of parameters are given so that the constructed functions are desired filled functions. 展开更多
关键词 Global optimization filled function nonsmooth optimization basin.
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一类非凸优化问题的邻近拟牛顿方法的复杂性
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作者 金玲子 《Chinese Quarterly Journal of Mathematics》 2023年第1期62-84,共23页
This paper studies a class of nonconvex composite optimization, whose objective is a summation of an average of nonconvex(weakly) smooth functions and a convex nonsmooth function, where the gradient of the former func... This paper studies a class of nonconvex composite optimization, whose objective is a summation of an average of nonconvex(weakly) smooth functions and a convex nonsmooth function, where the gradient of the former function has the H o¨lder continuity. By exploring the structure of such kind of problems, we first propose a proximal(quasi-)Newton algorithm wPQN(Proximal quasi-Newton algorithm for weakly smooth optimization) and investigate its theoretical complexities to find an approximate solution. Then we propose a stochastic variant algorithm wPSQN(Proximal stochastic quasi-Newton algorithm for weakly smooth optimization), which allows a random subset of component functions to be used at each iteration. Moreover, motivated by recent success of variance reduction techniques, we propose two variance reduced algorithms,wPSQN-SVRG and wPSQN-SARAH, and investigate their computational complexity separately. 展开更多
关键词 Nonconvex optimization nonsmooth optimization Holder continuity Proximal quasi-Newton Variance reduction
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A Feasible Point Method with Bundle Modification for Nonsmooth Convex Constrained Optimization 被引量:3
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作者 Jin-bao JIAN Chun-ming TANG Lu SHI 《Acta Mathematicae Applicatae Sinica》 SCIE CSCD 2018年第2期254-273,共20页
In this paper, a bundle modification strategy is proposed for nonsmooth convex constrained min- imization problems. As a result, a new feasible point bundle method is presented by applying this strategy. Whenever the ... In this paper, a bundle modification strategy is proposed for nonsmooth convex constrained min- imization problems. As a result, a new feasible point bundle method is presented by applying this strategy. Whenever the stability center is updated, some points in the bundle will be substituted by new ones which have lower objective values and/or constraint values, aiming at getting a better bundle. The method generates feasible serious iterates on which the objective function is monotonically decreasing. Global convergence of the algorithm is established, and some preliminary numerical results show that our method performs better than the standard feasible point bundle method. 展开更多
关键词 nonsmooth optimization feasible point method bundle modification global convergence
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A ONE-PARAMETER FILLED FUNCTION FOR NONSMOOTH GLOBAL OPTIMIZATION AND ITS APPLICATION 被引量:1
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作者 Ying ZHANG Liansheng ZHANG Yingtao XU 《Journal of Systems Science & Complexity》 SCIE EI CSCD 2010年第6期1195-1209,共15页
This paper presents a modified definition of the filled function for finding a global minimizer of a nonsmooth function on a closed bounded set, and then give a one-parameter filled function. Theoretical and numerical... This paper presents a modified definition of the filled function for finding a global minimizer of a nonsmooth function on a closed bounded set, and then give a one-parameter filled function. Theoretical and numerical properties of the proposed filled function are investigated and a corresponding solution algorithm is proposed. The proposed filled function's parameter is easier to be appropriately chosen than previous functions in literatures. Numerical results obtained indicate the efficiency of the proposed filled function method. An improved fingerprint recognition method using global filled function is also reported. 展开更多
关键词 Filled function global minimizer global optimization local minimizer nonsmooth optimization.
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A UV-decomposed method for solving an MPEC problem 被引量:1
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作者 单锋 庞丽萍 +1 位作者 朱丽梅 夏尊铨 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2008年第4期535-540,共6页
uv-decomposition method for solving a mathematical program with equilibrium constraints (MPEC) problem with linear complementarity constraints is presented. The problem is first converted into a nonlinear programmin... uv-decomposition method for solving a mathematical program with equilibrium constraints (MPEC) problem with linear complementarity constraints is presented. The problem is first converted into a nonlinear programming one. The structure of subdifferential a corresponding penalty function and results of its uv-decomposition are given. A conceptual algorithm for solving this problem with a superUnear convergence rate is then constructed in terms of the obtained results. 展开更多
关键词 nonsmooth optimization nonlinear programming subdifferential uv- decomposition u-Lagrangian MPEC problem
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Proximal Methods for Elliptic Optimal Control Problems with Sparsity Cost Functional 被引量:2
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作者 Andreas Schindele Alfio Borzì 《Applied Mathematics》 2016年第9期967-992,共26页
First-order proximal methods that solve linear and bilinear elliptic optimal control problems with a sparsity cost functional are discussed. In particular, fast convergence of these methods is proved. For benchmarking... First-order proximal methods that solve linear and bilinear elliptic optimal control problems with a sparsity cost functional are discussed. In particular, fast convergence of these methods is proved. For benchmarking purposes, inexact proximal schemes are compared to an inexact semismooth Newton method. Results of numerical experiments are presented to demonstrate the computational effectiveness of proximal schemes applied to infinite-dimensional elliptic optimal control problems and to validate the theoretical estimates. 展开更多
关键词 Optimal Control Elliptic PDE nonsmooth optimization Proximal Method Semismooth Newton Method
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SOME RESULTS ON OPTIMAL TOPOLOGY DESIGN OF TRUSS WITH UNILATERAL CONTACT CONSTRAINTS
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作者 Yang Deqing Liu Zhengxing Xuan Zhaocheng 《Acta Mechanica Solida Sinica》 SCIE EI 2000年第2期155-165,共11页
optimal topology design of truss structures concerning stress and frictionless unilateral contact displacement constraints is investigated. The existence of ununique optimal solution under contact gaps is found. This ... optimal topology design of truss structures concerning stress and frictionless unilateral contact displacement constraints is investigated. The existence of ununique optimal solution under contact gaps is found. This shows that the contact conditions have an effect on structural topology, and different initial contact gaps may lead to different structural topologies. To avoid the singular optima in structural topology optimization in multiple loading cases, an epsilon-relaxed method is adopted to establish the relaxing topology optimization formulations. The problem is solved by means of a two-level optimization method. In the first sublevel, the solution of the frictionless unilateral contact problem is obtained by solving an equivalent quadratic programming. In the second sublevel, topology optimization of truss is carried out by an epsilon-relaxed method. The validity of the method proposed is verified by computational results. 展开更多
关键词 structure optimization topology optimization CONTACT nonsmooth optimization
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A VU-decomposition method for a second-order cone programming problem
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作者 陆媛 庞丽萍 夏尊铨 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2010年第2期263-270,共8页
A vu-decomposition method for solving a second-order cone problem is presented in this paper. It is first transformed into a nonlinear programming problem. Then, the structure of the Clarke subdifferential correspondi... A vu-decomposition method for solving a second-order cone problem is presented in this paper. It is first transformed into a nonlinear programming problem. Then, the structure of the Clarke subdifferential corresponding to the penalty function and some results of itsvu-decomposition are given. Under a certain condition, a twice continuously differentiable trajectory is computed to produce a second-order expansion of the objective function. A conceptual algorithm for solving this problem with a superlinear convergence rate is given. 展开更多
关键词 second-order cone programming nonsmooth optimization vu-Lagrangian vu-decomposition
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On Optimal Sparse-Control Problems Governed by Jump-Diffusion Processes
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作者 Beatrice Gaviraghi Andreas Schindele +1 位作者 Mario Annunziato Alfio Borzì 《Applied Mathematics》 2016年第16期1978-2004,共27页
A framework for the optimal sparse-control of the probability density function of a jump-diffusion process is presented. This framework is based on the partial integro-differential Fokker-Planck (FP) equation that gov... A framework for the optimal sparse-control of the probability density function of a jump-diffusion process is presented. This framework is based on the partial integro-differential Fokker-Planck (FP) equation that governs the time evolution of the probability density function of this process. In the stochastic process and, correspondingly, in the FP model the control function enters as a time-dependent coefficient. The objectives of the control are to minimize a discrete-in-time, resp. continuous-in-time, tracking functionals and its L2- and L1-costs, where the latter is considered to promote control sparsity. An efficient proximal scheme for solving these optimal control problems is considered. Results of numerical experiments are presented to validate the theoretical results and the computational effectiveness of the proposed control framework. 展开更多
关键词 Jump-Diffusion Processes Partial Integro-Differential Fokker-Planck Equation Optimal Control Theory nonsmooth optimization Proximal Methods
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EXTENDED REGULARIZED DUAL AVERAGING METHODS FOR STOCHASTIC OPTIMIZATION
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作者 Jonathan W.Siegel Jinchao Xu 《Journal of Computational Mathematics》 SCIE CSCD 2023年第3期525-541,共17页
We introduce a new algorithm,extended regularized dual averaging(XRDA),for solving regularized stochastic optimization problems,which generalizes the regularized dual averaging(RDA)method.The main novelty of the metho... We introduce a new algorithm,extended regularized dual averaging(XRDA),for solving regularized stochastic optimization problems,which generalizes the regularized dual averaging(RDA)method.The main novelty of the method is that it allows a flexible control of the backward step size.For instance,the backward step size used in RDA grows without bound,while for XRDA the backward step size can be kept bounded.We demonstrate experimentally that additional control over the backward step size can speed up the convergence of the algorithm while preserving desired properties of the iterates,such as sparsity.Theoretically,we show that the XRDA method achieves the same convergence rate as RDA for general convex objectives. 展开更多
关键词 Convex optimization Subgradient Methods Structured optimization nonsmooth optimization
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Characterizing Shadow Price via Lagrange Multiplier for Nonsmooth Problem
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作者 Yan Gao 《Journal of the Operations Research Society of China》 EI CSCD 2023年第4期827-838,共12页
In this paper,the relation between the shadow price and the Lagrange multiplier for nonsmooth optimization problem is explored.It is obtained that the Lagrange multipliers are upper bounds of the shadow price for a co... In this paper,the relation between the shadow price and the Lagrange multiplier for nonsmooth optimization problem is explored.It is obtained that the Lagrange multipliers are upper bounds of the shadow price for a convex optimization problem and a class of Lipschtzian optimization problems.This result can be used in pricing mechanisms for nonsmooth situation.Several nonsmooth functions involved in this class of Lipschtzian optimizations are listed.Finally,an application to electricity pricing is discussed. 展开更多
关键词 Shadow price Lagrange multiplier nonsmooth optimization
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On the local convergence of a stochastic semismooth Newton method for nonsmooth nonconvex optimization 被引量:1
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作者 Andre Milzarek Xiantao Xiao +1 位作者 Zaiwen Wen Michael Ulbrich 《Science China Mathematics》 SCIE CSCD 2022年第10期2151-2170,共20页
In this work,we present probabilistic local convergence results for a stochastic semismooth Newton method for a class of stochastic composite optimization problems involving the sum of smooth nonconvex and nonsmooth c... In this work,we present probabilistic local convergence results for a stochastic semismooth Newton method for a class of stochastic composite optimization problems involving the sum of smooth nonconvex and nonsmooth convex terms in the objective function.We assume that the gradient and Hessian information of the smooth part of the objective function can only be approximated and accessed via calling stochastic firstand second-order oracles.The approach combines stochastic semismooth Newton steps,stochastic proximal gradient steps and a globalization strategy based on growth conditions.We present tail bounds and matrix concentration inequalities for the stochastic oracles that can be utilized to control the approximation errors via appropriately adjusting or increasing the sampling rates.Under standard local assumptions,we prove that the proposed algorithm locally turns into a pure stochastic semismooth Newton method and converges r-linearly or r-superlinearly with high probability. 展开更多
关键词 nonsmooth stochastic optimization stochastic approximation semismooth Newton method stochastic second-order information local convergence
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A note on a family of proximal gradient methods for quasi-static incremental problems in elastoplastic analysis
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作者 Yoshihiro Kanno 《Theoretical & Applied Mechanics Letters》 CAS CSCD 2020年第5期315-320,共6页
Accelerated proximal gradient methods have recently been developed for solving quasi-static incremental problems of elastoplastic analysis with some different yield criteria.It has been demonstrated through numerical ... Accelerated proximal gradient methods have recently been developed for solving quasi-static incremental problems of elastoplastic analysis with some different yield criteria.It has been demonstrated through numerical experiments that these methods can outperform conventional optimization-based approaches in computational plasticity.However,in literature these algorithms are described individually for specific yield criteria,and hence there exists no guide for application of the algorithms to other yield criteria.This short paper presents a general form of algorithm design,independent of specific forms of yield criteria,that unifies the existing proximal gradient methods.Clear interpretation is also given to each step of the presented general algorithm so that each update rule is linked to the underlying physical laws in terms of mechanical quantities. 展开更多
关键词 Elastoplastic analysis Incremental problem nonsmooth convex optimization First-order optimization method Proximal gradient method
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