检索结果-内蒙古大学图书馆

A generalization of linearized alternating direction method of multipliers for solving two-block separable convex programming

引用

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS 2019年 357卷 251-272页

作者： Chang, Xiaokai Liu, Sanyang Zhao, Pengjun Song, Dunjiang Xidian Univ Sch Math & Stat Xian 710071 Peoples R China Lanzhou Univ Technol Coll Sci Lanzhou 730050 Gansu Peoples R China Shangluo Univ Sch Math & Comp Applicat Shangluo 726000 Peoples R China Chinese Acad Sci Inst Sci Beijing 100190 Peoples R China Chinese Acad Sci Inst Dev Beijing 100190 Peoples R China

The linearized alternating direction method of multipliers (ADMM), with indefinite proximal regularization, has been proved to be efficient for solving separable convex optimization subject to linear constraints. In this paper, we present a generalization of linearized ADMM (G-LADMM) to solve two-block separable convex minimization model, which linearizes all the subproblems by choosing a proper positive-definite or indefinite proximal term and updates the Lagrangian multiplier twice in different ways. Furthermore, the proposed G-LADMM can be expressed as a proximal point algorithm (PPA), and all the subproblems are just to estimate the proximity operator of the function in the objective. We specify the domain of the proximal parameter and stepsizes to guarantee that G-LADMM is globally convergent. It turns out that our convergence domain of the proximal parameter and stepsizes is significantly larger than other convergence domains in the literature. The numerical experiments illustrate the improvements of the proposed G-LADMM to solve LASSO and image decomposition problems. (C) 2019 Elsevier B.V. All rights reserved.

关键词： Alternating direction method of multipliers Proximal point algorithm separable convex programming Linearization Indefinite proximal regularization LASSO

来源：评论

学校读者我要写书评

暂无评论

Explicit model of dual programming and solving method for a class of separable convex programming problems

引用

ENGINEERING OPTIMIZATION 2019年第9期51卷 1604-1625页

作者： Sui, YunKang Peng, XiRong Beijing Univ Technol Numer Simulat Ctr Engn Beijing Peoples R China Hunan City Univ Sch Civil Engn Yiyang Peoples R China

An objective function for a dual model of nonlinear programming problems is an implicit function with respect to Lagrangian multipliers. This study aims to address separable convex programming problems. An explicit expression with respect to Lagrangian multipliers is derived for the dual objective function. The exact solution of the dual model can be achieved because an explicit objective function is more exact than an approximated objective function. Then, a set of improved Lagrangian multipliers can be used to obtain the optimal solution of the original nonlinear programming model. A corresponding dual programming and explicit model (DP-EM) method is proposed and applied to the structural topology optimization of continuum structures. The solution efficiency of the DPEM is compared with the dual sequential quadratic programming (DSQP) method and method of moving asymptotes (MMA). The results show that the DP-EM method is more efficient than the DSQP and MMA.

关键词： Explicit dual objective function separable convex programming structural topology optimization dual sequential quadratic programming (DSQP) method method of moving asymptotes (MMA)

来源：评论

学校读者我要写书评

暂无评论

Duality Theorems for separable convex programming Without Qualifications

引用

JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS 2017年第2期172卷 669-683页

作者： Suzuki, Satoshi Kuroiwa, Daishi Shimane Univ Dept Math Matsue Shimane Japan

In the research of mathematical programming, duality theorems are essential and important elements. Recently, Lagrange duality theorems for separable convex programming have been studied. Tseng proves that there is no duality gap in Lagrange duality for separable convex programming without any qualifications. In other words, although the infimum value of the primal problem equals to the supremum value of the Lagrange dual problem, Lagrange multiplier does not always exist. Jeyakumar and Li prove that Lagrange multiplier always exists without any qualifications for separable sublinear programming. Furthermore, Jeyakumar and Li introduce a necessary and sufficient constraint qualification for Lagrange duality theorem for separable convex programming. However, separable convex constraints do not always satisfy the constraint qualification, that is, Lagrange duality does not always hold for separable convex programming. In this paper, we study duality theorems for separable convex programming without any qualifications. We show that a separable convex inequality system always satisfies the closed cone constraint qualification for quasiconvex programming and investigate a Lagrange-type duality theorem for separable convex programming. In addition, we introduce a duality theorem and a necessary and sufficient optimality condition for a separable convex programming problem, whose constraints do not satisfy the Slater condition.

关键词： separable convex programming Duality theorem Constraint qualification Generator of quasiconvex functions

来源：评论

学校读者我要写书评

暂无评论

Risk management in herd sire portfolio selection: A comparison of rounded quadratic and separable convex programming

引用

JOURNAL OF DAIRY SCIENCE 1996年第2期79卷 301-309页

作者： Nash, DL Rogers, GW Nash DL PENN STATE UNIV DEPT DAIRY & ANIM SCI UNIVERSITY PK PA 16802 USA

Quadratic programming, which does not guarantee integer solutions, may be used to consider risk when herd sires are selected. Because semen cannot be purchased in partial units, two alternatives were investigated: separable convex programming (a linear approximation of quadratic programming) and rounded quadratic programming. Expected net revenue and its variance were calculated for 383 Holstein bulls. Expected net revenue was based on semen price;PTA dollars for milk, fat, and protein;and three linear type traits: foot angle, udder depth, and teat placement. Maximization of utility (expected net revenue less its variance times a risk aversion factor) was subject to constraints: lots of 5 units, maximum average price per lot, minimum number of lots from bulls that transmit calving ease, and minimum number of different sires of selected bulls. Multiple formulations for expected net revenue, constraint combinations, and risk aversion factors were used. Twenty-two of 60 pairs of sire portfolios from rounded quadratic and separable convex programming were identical. Semen price per lot and lots from bulls that transmit calving ease were influential constraints. At the two lowest amounts of risk aversion examined, results supported common recommendations of selection of three to seven herd sires, regardless of herd size.

关键词： sire selection risk management quadratic programming separable convex programming

来源：评论

学校读者我要写书评

暂无评论

A Two-Segment Approximation Algorithm for separable convex programming with Linear Constraints

引用

Optimization 1986年第2期17卷 147-159页

作者： Ali, I. Charnes, A. Song, T. University of Texas at Austin Graduate School of Business Center for Cybernetic Studies Texas United States

We discuss a new algorithm for the separable convex programming with linear constraints. This is based on the approximation of the objective function by at most two linear pieces in the neighborhood of the current feasible solution. The two segments will be adaptively defined rather than predecided fixed grids. If, furthermore, the objective function is differentiable, and one introduces a non-Archimedean infinitesimal, the algorithm generates a sequence of feasible solutions every cluster point of which is an optimal solution. Computational tests on the problem with up to 106 non linear variables are presented. © 1986, Taylor & Francis Group, LLC. All rights reserved.

关键词： separable convex programming Two-segment approximation

来源：评论

学校读者我要写书评

暂无评论

A set of linearised partially-parallel splitting methods for separable convex programs

引用

IIMB MANAGEMENT REVIEW 2025年第1期37卷

作者： Desai, Jitamitra Wang, Kai Indian Inst Management Bangalore Bangalore India Nanjing Univ Sci & Technol Sch Sci Nanjing Peoples R China

The proximal partially-parallel splitting method (PPSM), originally proposed in Wang, Desai, and He (2017), is a hybrid mechanism that inherits the nice properties of both Gauss-Seidel and Jacobian substitution procedures for solving the multiple-block convex minimisation problem, whose objective function is the sum of m individual (separable) functions without any shared variables, subject to a linear coupling constraint. In this paper, we extend this work and present some linearised versions of the PPSM, which fully utilise the separable structure and result in subproblems that either have closed-form solutions or are relatively easy to solve as compared to their original nonlinear versions. Global convergence of these linearised methods under the projection contraction algorithmic framework is proven, and furthermore, detailed remarks that serve to clarify the interconnections between these linearised variants are highlighted. Finally, the worstcase O(1=t) convergence rate of these methods under ergodic conditions is also established. (c) 2024 Published by Elsevier Ltd on behalf of Indian Institute of Management Bangalore. This is an open access article under the CC BY-NC-ND license (http://***/licenses/by-ncnd/4.0/)

关键词： Augmented Lagrangian method separable convex programming Proximal partially- parallel splitting method (PPSM) Linearisation techniques Global convergence Convergence rate

来源：评论

学校读者我要写书评

暂无评论

APPLICATIONS OF THE METHOD OF PARTIAL INVERSES TO convex-programming - DECOMPOSITION

引用

MATHEMATICAL programming 1985年第2期32卷 199-223页

作者： SPINGARN, JE 1.School of Mathematics Georgia Institute of Technology 30332 Atlanta GA USA

A primal–dual decomposition method is presented to solve the separable convex programming problem. Convergence to a solution and Lagrange multiplier vector occurs from an arbitrary starting point. The method is equivalent to the proximal point algorithm applied to a certain maximal monotone multifunction. In the nonseparable case, it specializes to a known method, the proximal method of multipliers. Conditions are provided which guarantee linear convergence.

关键词： Monotone Multifunction separable convex programming Proximal Point Algorithm Decomposition Algorithm Resource Allocation Large-Scale programming

来源：评论

学校读者我要写书评

暂无评论

A parameterized proximal point algorithm for separable convex optimization

引用

OPTIMIZATION LETTERS 2018年第7期12卷 1589-1608页

作者： Bai, Jianchao Zhang, Hongchao Li, Jicheng Xi An Jiao Tong Univ Sch Math & Stat Xian 710049 Shaanxi Peoples R China Louisiana State Univ Dept Math Baton Rouge LA 70803 USA

In this paper, we develop a parameterized proximal point algorithm (P-PPA) for solving a class of separable convex programming problems subject to linear and convex constraints. The proposed algorithm is provable to be globally convergent with a worst-case O(1/t) convergence rate, where t denotes the iteration number. By properly choosing the algorithm parameters, numerical experiments on solving a sparse optimization problem arising from statistical learning show that our P-PPA could perform significantly better than other state-of-the-art methods, such as the alternating direction method of multipliers and the relaxed proximal point algorithm.

关键词： separable convex programming Proximal point algorithm Global convergence Statistical learning

来源：评论

学校读者我要写书评

暂无评论

Managing inventory with multiple products, lags in delivery, resource constraints, and lost sales: A mathematical programming approach

引用

MANAGEMENT SCIENCE 2001年第3期47卷 464-479页

作者： Downs, B Metters, R Semple, J Aspen Technol Inc Supply Chain Div Houston TX 77077 USA So Methodist Univ Edwin L Cox Sch Business Dept Informat Syst & Operat Management Dallas TX 75275 USA

This paper develops an order-up-to S inventory model that is designed to handle multiple items, resource constraints, lags in delivery, and lost sales without sacrificing computational simplicity. Mild conditions are shown to ensure that the expected average holding cost and the expected average shortage cost are separable convex functions of the order-up-to levels. We develop nonparametric estimates of these costs and use them in conjunction with Linear programming to produce what is termed the "LP policy." The LP policy has two major advantages over traditional methods: first, it can be computed in complex environments such as the one described above;and second, it does not require an explicit functional form of demand, something that is difficult to specify accurately in practice. In two numerical experiments designed so that optimal policies could be computed, the LP policy fared well, differing from the optimal profit by an average of 2.20% and 1.84%, respectively. These results compare quite favorably with the errors incurred in traditional methods when a correctly specified distribution uses estimated parameters. Our findings support the effectiveness of this mathematical programming technique for approximating complex, real-world inventory control problems.

关键词： inventory heuristic approximation nonparametric estimation separable convex programming linear programming

来源：评论

学校读者我要写书评

暂无评论

A minimum mean cycle cancelling method for nonlinear multicommodity flow problems

引用

EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2000年第3期121卷 532-548页

作者： Ouorou, A Mahey, P Univ Blaise Pascal Lab Informat Modelisat & Optimisat Syst ISIMA F-63173 Aubiere France

We propose a neu method based on minimum mean cycle cancelling for multicommodity flow problems with separable convex cost ruling out saturated capacities. This method is inspired by the cycle cancelling method first worked out by Goldberg and Tarjan for minimum cost circulations (A.V. Goldberg, R.E. Tarjan, Finding minimum-cost circulation by cancelling negative cycles, JACM 36 (4), 1989, pp. 873-886). Convergence of the method is formally proved and a variant with a more flexible selection of cycles is proposed. Also. we report some computational experience on the message routing problem in telecommunication networks using actual and randomly generated networks. (C) 2000 Elsevier Science B.V. All rights reserved.

关键词： network programming multicommodity flows cycle cancelling methods separable convex programming

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：