检索结果-内蒙古大学图书馆

Convergence Analysis of the Generalized Splitting Methods for a Class of nonconvex optimization problems

JOURNAL OF optimization THEORY AND APPLICATIONS 2019年第2期183卷 535-565页

作者： Li, Min Wu, Zhongming Nanjing Univ Sch Management & Engn Nanjing 210093 Jiangsu Peoples R China Southeast Univ Sch Econ & Management Nanjing 210096 Jiangsu Peoples R China

In this paper, we propose generalized splitting methods for solving a class of nonconvex optimization problems. The new methods are extended from the classic Douglas-Rachford and Peaceman-Rachford splitting methods. The range of the new step-sizes even can be enlarged two times for some special cases. The new methods can also be used to solve convex optimization problems. In particular, for convex problems, we propose more relax conditions on step-sizes and other parameters and prove the global convergence and iteration complexity without any additional assumptions. Under the strong convexity assumption on the objective function, the linear convergence rate can be derived easily.

关键词： Competing structure Lipschitz continuous nonconvex optimization problems Splitting methods Step-size

来源：评论

学校读者我要写书评

暂无评论

Peaceman-Rachford splitting for a class of nonconvex optimization problems

引用

COMPUTATIONAL optimization AND APPLICATIONS 2017年第2期68卷 407-436页

作者： Li, Guoyin Liu, Tianxiang Pong, Ting Kei Univ New South Wales Dept Appl Math Sydney NSW 2052 Australia Hong Kong Polytech Univ Dept Appl Math Hong Kong Hong Kong Peoples R China

We study the applicability of the Peaceman-Rachford (PR) splitting method for solving nonconvex optimization problems. When applied to minimizing the sum of a strongly convex Lipschitz differentiable function and a proper closed function, we show that if the strongly convex function has a large enough strong convexity modulus and the step-size parameter is chosen below a threshold that is computable, then any cluster point of the sequence generated, if exists, will give a stationary point of the optimization problem. We also give sufficient conditions guaranteeing boundedness of the sequence generated. We then discuss one way to split the objective so that the proposed method can be suitably applied to solving optimization problems with a coercive objective that is the sum of a (not necessarily strongly) convex Lipschitz differentiable function and a proper closed function;this setting covers a large class of nonconvex feasibility problems and constrained least squares problems. Finally, we illustrate the proposed algorithm numerically.

关键词： Peaceman-Rachford splitting Feasibility problems nonconvex optimization problems Global convergence

来源：评论

学校读者我要写书评

暂无评论

Regularized Nesterov's accelerated damped BFGS method for stochastic optimization

引用

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS 2025年 467卷

作者： Suppalap, Siwakon Makmuang, Dawrawee Damminsed, Vipavee Wangkeeree, Rabian Naresuan Univ Fac Sci Dept Math Phitsanulok 65000 Thailand Naresuan Univ Res Ctr Acad Excellence Math Phitsanulok 65000 Thailand

A regularization term is introduced into the approximate Hessian update in the stochastic Broyden-Fletcher-Goldfarb-Shanno (BFGS) method for convex stochastic optimization problems to help avoid near-singularity issues. Additionally, Nesterov acceleration, with a momentum coefficient that dynamically adjusts between a constant value and zero based on the objective function, has been incorporated to enhance convergence speed. However, the inflexibility of the constant momentum coefficient still may lead to overshooting problems, and evaluating objective functions on large datasets is computationally costly. Moreover, this approach presents challenges in solving nonconvex optimization problems. To address these challenges, we propose a regularized stochastic BFGS method that integrates Nesterov acceleration with an adaptive momentum coefficient designed for solving nonconvex stochastic optimization problems. This coefficient adjusts flexibly between a decreasing value and zero based on selected dataset samples, helping to avoid overshooting problems and reduce computational costs. We demonstrated almost sure convergence to stationary points and analyze the complexity. Numerical results on convex and nonconvex classification problems using a support vector machine show that our method outperforms existing approaches.

关键词： Nesterov acceleration Stochastic BFGS method Convex optimization problems nonconvex optimization problems

来源：评论

学校读者我要写书评

暂无评论

Primal-Dual Trust-Region Methods for Nonlinear Programming

Primal-Dual Trust-Region Methods for Nonlinear Programming

引用

作者： Huang, Yesheng University of California San Diego

学位级别：Ph.D., Doctor of Philosophy

The goal of this dissertation is to investigate the formulation and analysis of a trust-region interior-point method for solving nonconvex optimization problems with a mixture of equality and inequality constraints. The proposed method is based on minimizing a merit function that may be interpreted as a shifted primal-dual penalty-barrier function. The method generates a sequence of iterates with limit points that are either infeasible stationary points or complementary approximate Karush-Kuhn-Tucker points, i.e., every limit point satisfies reasonable stopping criteria and is a Karush-Kuhn-Tucker point under a regularity condition that is the weakest constraint qualification associated with sequential optimality conditions. Under suitable additional assumptions, the method is equivalent to a shifted variant of the primal-dual path-following method in the neighborhood of a solution. The proposed method has an inner/outer iteration structure. The outer iteration specifies the form of the merit function. The inner iteration optimizes the merit function with fixed parameters using a trust-region method. The algorithm for solving the trust-region subproblem involves a procedure based on the application of a one-dimensional Newton’s method. Methods are proposed for treating the so-called ”hard case” in which no root of the one dimensional equation exists.

关键词： Nonlinear programming nonconvex optimization problems Inequality constraints Karush-Kuhn-Tucker points Merit function

来源：评论

学校读者我要写书评

暂无评论

Minimal energy configurations of bilayer plates as a polynomial optimization problem

引用

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS 2023年 231卷

作者： Mohan, Preetham Yip, Nung Kwan Yu, Thomas Univ Michigan Dept Math Ann Arbor MI USA Purdue Univ Dept Math W Lafayette IN 47907 USA Drexel Univ Dept Math Philadelphia PA USA

We develop a discretization method for solving the minimal energy configuration of bilayer plates based on a mathematical model developed in Schmidt (2007), Bartels et al. (2017). Our discretization method employs C1-spline functions. A highlight of the method involves a trick to handle the nonlinear isometry constraint in such a way that not only numerical integration becomes unnecessary, but also that the final optimization problems are in the form of degree 4 polynomial optimization problems (POP). We develop two different versions of the method, one resulted in a constrained degree 4 POP involving a small tolerance e, another resulted in an unconstrained degree 4 POP involving a large penalty parameter mu. We develop a mathematical analysis, based on the direct method and techniques in G-convergence, to show how e and mu can be chosen according to the grid size so that the minimizers of the discrete problems converge to that of the continuum variational problem as the grid size goes to zero. We corroborate the theory through a series of computational experiments, and also report an unexpected finding related to the asymmetry of the discretized problems. (c) 2022 Elsevier Ltd. All rights reserved.

关键词： Bilayer plates Splines Calculus of variation G-convergence Sparse polynomial optimization problems nonconvex optimization problems

来源：评论

学校读者我要写书评

暂无评论

A modified Broyden family algorithm with global convergence under a weak Wolfe-Powell line search for unconstrained nonconvex problems

引用

CALCOLO 2020年第4期57卷 35-35页

作者： Yuan, Gonglin Wang, Zhan Li, Pengyuan Guangxi Univ Coll Math & Informat Sci Nanning Peoples R China

The Quasi-Newton method is one of the most effective methods using the first derivative for solving all unconstrained optimization problems. The Broyden family method plays an important role among the quasi-Newton algorithms. However, the study of the convergence of the classical Broyden family method is still not enough. While in the special case, BFGS method, there have been abundant achievements. Yuan et al. (Appl Math Model. 47:811-825, (2017)) presented a modified weak Wolfe-Powell line search and obtained the convergence of BFGS method for general functions under this line search. Motivated by their works, a new modified weak Wolfe-Powell line search technique is proposed for unconstrained problems. We assume that the objective function is nonconvex and the global convergence of the restricted Broyden family method is established. Preliminary numerical results including the classical optimization problems and the Muskingum model show that the presented algorithm is promising.

关键词： Broyden family method Weak Wolfe line search Global convergence nonconvex optimization problems

来源：评论

学校读者我要写书评

暂无评论

A parameterized Douglas-Rachford splitting algorithm for nonconvex optimization

引用

APPLIED MATHEMATICS AND COMPUTATION 2021年 410卷 126425-126425页

作者： Bian, Fengmiao Zhang, Xiaoqun Shanghai Jiao Tong Univ Sch Math Sci Shanghai 200240 Peoples R China Shanghai Jiao Tong Univ Inst Nat Sci Shanghai 200240 Peoples R China

In this paper, we study a parameterized Douglas-Rachford splitting method in Wang-Wang (2019)[5] for a class of nonconvex optimization problem. A new merit function is constructed to establish the convergence of the whole sequence generated by the parameterized Douglas-Rachford splitting method. As a by-product, this also provides convergence results of a special case of the adaptive Douglas-Rachford algorithm proposed by Dao and Phan (2019)[22] in nonconvex settings. We then apply the parameterized Douglas-Rachford splitting method to three important classes of nonconvex optimization problems arising in data science: sparsity constrained least squares problem, feasibility problem and low rank matrix completion. Numerical results validate the effectiveness of the parameterized Douglas-Rachford splitting method compared with some other classical methods. (c) 2021 Elsevier Inc. All rights reserved.

关键词： Parameterized Douglas-Rachford splitting method nonconvex optimization problems Global convergence Sparsity constrained least squares problem Low rank matrix completion Feasibility problem

来源：评论

学校读者我要写书评

暂无评论

OpEn: Code Generation for Embedded nonconvex optimization 21st

OpEn: Code Generation for Embedded Nonconvex Optimization

引用

21st IFAC World Congress on Automatic Control - Meeting Societal Challenges

作者： Sopasakis, Pantelis Fresk, Emil Patrinos, Panagiotis Queens Univ Belfast Sch Elect Elect Engn & Comp Sci EEECS Ashby BldgStranmillis Rd Belfast BT9 5AG Antrim North Ireland Queens Univ Belfast Ctr Intelligent & Autonomous Mfg Syst I AMS Ashby BldgStranmillis Rd Belfast BT9 5AG Antrim North Ireland WideFind AB Aurorum 1C S-97775 Lulea Sweden Katholieke Univ Leuven Dept Elect Engn ESAT STADIUS Ctr Dynam Syst Signal Proc & Data Analyt Kasteelpk Arenberg 10 B-3001 Leuven Belgium Katholieke Univ Leuven Optimizat Engn OPTEC Kasteelpk Arenberg 10 B-3001 Leuven Belgium

We present optimization Engine (OpEn): an open-source code generation framework for real-time embedded nonconvex optimization, which implements a novel numerical method. OpEn combines the proximal averaged Newton-type method for optimal control (PANOC) with the penalty and augmented Lagrangian methods to compute approximate stationary points of nonconvex problems. The proposed method involves very simple algebraic operations such as vector products, has a low memory footprint and exhibits very good convergence properties that allow the solution of nonconvex problems on embedded devices. OpEn's core solver is written is Rust a modern, high-performance, memory-safe and thread-safe systems programming language while users can call it from Python, MATLAB, C, C++, ROS or over a TCP socket. Copyright (C) 2020 The Authors.

关键词： Embedded numerical optimization nonconvex optimization problems code generation model predictive control moving horizon estimation Rust Robot Operating System

来源：评论

学校读者我要写书评

暂无评论

A regularized alternating direction method of multipliers for a class of nonconvex problems

引用

JOURNAL OF INEQUALITIES AND APPLICATIONS 2019年第1期2019卷 1-16页

作者： Jian, Jin Bao Zhang, Ye Chao, Mian Tao Guangxi Univ Coll Math & Informat Sci Nanning Peoples R China Guangxi Univ Nationalities Coll Sci Nanning Peoples R China

In this paper, we propose a regularized alternating direction method of multipliers (RADMM) for a class of nonconvex optimization problems. The algorithm does not require the regular term to be strictly convex. Firstly, we prove the global convergence of the algorithm. Secondly, under the condition that the augmented Lagrangian function satisfies the Kurdyka-ojasiewicz property, the strong convergence of the algorithm is established. Finally, some preliminary numerical results are reported to support the efficiency of the proposed algorithm.

关键词： nonconvex optimization problems Alternating direction method of multipliers Kurdyka-ojasiewicz property Convergence

来源：评论

学校读者我要写书评

暂无评论

OpEn: Code Generation for Embedded nonconvex optimization *

引用

IFAC-PapersOnLine 2020年第2期53卷 6548-6554页

作者： Pantelis Sopasakis Emil Fresk Panagiotis Patrinos Queen’s University Belfast School of Electronics Electrical Engineering and Computer Science (EEECS) and Centre for Intelligent and Autonomous Manufacturing Systems (i-AMS) Ashby Building Stranmillis Road BT9 5AG Belfast Northern Ireland WideFind AB Aurorum 1C 977 75 Luleå Sweden KU Leuven Department of Electrical Engineering (ESAT) STADIUS Center for Dynamical Systems Signal Processing and Data Analytics & Optimization in Engineering (OPTEC) Kasteelpark Arenberg 10 3001 Leuven Belgium

We present optimization Engine (OpEn): an open-source code generation framework for real-time embedded nonconvex optimization, which implements a novel numerical method. OpEn combines the proximal averaged Newton-type method for optimal control (PANOC) with the penalty and augmented Lagrangian methods to compute approximate stationary points of nonconvex problems. The proposed method involves very simple algebraic operations such as vector products, has a low memory footprint and exhibits very good convergence properties that allow the solution of nonconvex problems on embedded devices. OpEn’s core solver is written is Rust — a modern, high-performance, memory-safe and thread-safe systems programming language — while users can call it from Python, MATLAB, C, C++, ROS or over a TCP socket.

关键词： Embedded numerical optimization nonconvex optimization problems code generation model predictive control moving horizon estimation Rust Robot Operating System

来源：评论

学校读者我要写书评

暂无评论

建议与咨询留下您的常用邮箱和电话号码，以便我们向您反馈解决方案和替代方法

时间限定

文献类型

馆藏选择

核心期刊

语言

文献类型

帮助

文字说明：

检索规则说明：

检索范例：

分类表

所选分类

限定检索结果

文献类型

馆藏范围

日期分布

学科分类号

主题

机构

作者

语言

请选择保存的检索档案：

请选择收藏分类：

通借通还

建议与咨询 留下您的常用邮箱和电话号码，以便我们向您反馈解决方案和替代方法

时间限定

文献类型

馆藏选择

核心期刊

语言

文献类型

帮助

文字说明：

检索规则说明：

检索范例：

分类表

所选分类

限定检索结果

文献类型

馆藏范围

日期分布

学科分类号

主题

机构

作者

语言

请选择保存的检索档案： 新增检索档案 确定 取消

请选择收藏分类： 新增自定义分类 确定 取消

通借通还

建议与咨询留下您的常用邮箱和电话号码，以便我们向您反馈解决方案和替代方法

请选择保存的检索档案：

请选择收藏分类：