检索结果-内蒙古大学图书馆

A Neurodynamic Approach for Solving robust linear programming under the Polyhedral Uncertainty Set

NEURAL PROCESSING LETTERS 2023年第8期55卷 10669-10683页

作者： Hu, Jin He, Li Peng, Yiheng Zeng, Chunna Chongqing Jiaotong Univ Sch Math & Stat Chongqing 400074 Peoples R China Chongqing Normal Univ Coll Math Sci Chongqing 401331 Peoples R China

This paper converts the robust linear programming under the polyhedral uncertainty set to standard linear programming. After eliminating the parameter uncertainty, we design a projection neural network to address the problem. The equilibrium point of the neural network model is theoretically proved to be stable in the Lyapunov sense and globally convergent to the optimal solution to robust linear programming. Two numerical examples are provided to illustrate the validity and performance of the proposed approach.

关键词： robust linear programming Polyhedral uncertainty set Neurodynamic approach Lyapunov function Global convergence

来源：评论

学校读者我要写书评

暂无评论

Randomized Constraints Consensus for Distributed robust linear programming

引用

IFAC-PapersOnLine 2017年第1期50卷 4973-4978页

作者： Chamanbaz M. Notarstefano G. Bouffanais R. Arak University of Technology Arak Iran Singapore University of Technology and Design Singapore Department of Engineering Università del Salento Lecce Italy

In this paper we consider a network of processors aiming at cooperatively solving linear programming problems subject to uncertainty. Each node only knows a common cost function and its local uncertain constraint set. We propose a randomized, distributed algorithm working under time-varying, asynchronous and directed communication topology. The algorithm is based on a local computation and communication paradigm. At each communication round, nodes perform two updates: (i) a verification in which they check—in a randomized setup—the robust feasibility (and hence optimality) of the candidate optimal point, and (ii) an optimization step in which they exchange their candidate bases (minimal sets of active constraints) with neighbors and locally solve an optimization problem whose constraint set includes: a sampled constraint violating the candidate optimal point (if it exists), agent's current basis and the collection of neighbor's basis. As main result, we show that if a processor successfully performs the verification step for a sufficient number of communication rounds, it can stop the algorithm since a consensus has been reached. The common solution is—with high confidence—feasible (and hence optimal) for the entire set of uncertainty except a subset having arbitrary small probability measure. We show the effectiveness of the proposed distributed algorithm on a multi-core platform in which the nodes communicate asynchronously. © 2017

关键词： control of large-scale network systems Distributed Optimization Large scale optimization problems Optimization Randomized Algorithms robust linear programming

来源：评论

学校读者我要写书评

暂无评论

Randomized Constraints Consensus for Distributed robust linear programming

Randomized Constraints Consensus for Distributed Robust Line...

引用

20th World Congress of the International-Federation-of-Automatic-Control (IFAC)

作者： Chamanbaz, Mohammadreza Notarstefano, Giuseppe Bouffanais, Roland Arak Univ Technol Arak Iran Univ Salento Dept Engn Lecce Italy Singapore Univ Technol & Design Singapore Singapore

In this paper we consider a network of processors aiming at cooperatively solving linear programming problems subject to uncertainty. Each node only knows a common cost function and its local uncertain constraint set. We propose a randomized, distributed algorithm working under time-varying, asynchronous and directed communication topology. The algorithm is based on a local computation and communication paradigm. At each communication round, nodes perform two updates: (i) a verification in which they check in a randomized setup the robust feasibility (and hence optimality) of the candidate optimal point, and (ii) an optimization step in which they exchange their candidate bases (minimal sets of active constraints) with neighbors and locally solve an optimization problem whose constraint set includes: a sampled constraint violating the candidate optimal point (if it exists), agent's current basis and the collection of neighbor's basis. As main result, we show that if a processor successfully performs the verification step for a sufficient number of communication rounds, it can stop the algorithm since a consensus has been reached. The common solution is with high confidence feasible (and hence optimal) for the entire set of uncertainty except a subset having arbitrary small probability measure. We show the effectiveness of the proposed distributed algorithm on a multi-core platform in which the nodes communicate asynchronously. (C) 2017, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved.

关键词： Distributed Optimization Randomized Algorithms robust linear programming Optimization and control of large-scale network systems Large scale optimization problems

来源：评论

学校读者我要写书评

暂无评论

Formal Multi-Objective Synthesis of Continuous-State MDPs

引用

IEEE CONTROL SYSTEMS LETTERS 2021年第5期5卷 1765-1770页

作者： Haesaert, Sofie Nilsson, Petter Soudjani, Sadegh Eindhoven Univ Technol Dept Elect Engn NL-5612 Eindhoven Netherlands Yamaha Motor Corp Boat Power Syst Div Kennesaw GA 30144 USA Newcastle Univ Sch Comp Newcastle Upon Tyne NE4 5TG Tyne & Wear England

This letter studies formal synthesis of control policies for continuous-state MDPs. In the quest to satisfy complex combinations of probabilistic temporal logic specifications, we derive a robust linear program for policy synthesis that is solved on a finite-state approximation of the system and is then refined back to a policy for the original system. This linear programming approach leverages occupation measures and enables the multi-objective optimizations needed to handle more complex probabilistic specifications.

关键词： Probabilistic logic Computational modeling Markov processes Labeling Optimization Measurement uncertainty Loss measurement Approximate simulation relations formal synthesis stochastic systems robust linear programming temporal logic

来源：评论

学校读者我要写书评

暂无评论

Exact relaxations for parametric robust linear optimization problems

引用

OPERATIONS RESEARCH LETTERS 2019年第2期47卷 105-109页

作者： Thai Doan Chuong Ton Duc Thang Univ Optimizat & Applicat Res Grp Ho Chi Minh City Vietnam Ton Duc Thang Univ Fac Math & Stat Ho Chi Minh City Vietnam

We first show that the closedness of the characteristic cone of the constraint system of a parametric robust linear optimization problem is a necessary and sufficient condition for each robust linear program with the finite optimal value to admit exact semidefinite linear programming relaxations. We then provide the weakest regularity condition that guarantees exact second-order cone programming relaxations for parametric robust linear programs. (C) 2019 Elsevier B.V. All rights reserved.

关键词： Semi-infinite programming Relaxation Semidefinite linear program robust linear programming Parametric optimization problem

来源：评论

学校读者我要写书评

暂无评论

A robust optimization methodology for preliminary aircraft design

引用

ENGINEERING OPTIMIZATION 2016年第5期48卷 883-899页

作者： Prigent, S. Marechal, P. Rondepierre, A. Druot, T. Belleville, M. AIRBUS Future Project Off Toulouse France Univ Toulouse Inst Math Toulouse Toulouse France INSA Toulouse France

This article focuses on a robust optimization of an aircraft preliminary design under operational constraints. According to engineers' know-how, the aircraft preliminary design problem can be modelled as an uncertain optimization problem whose objective (the cost or the fuel consumption) is almost affine, and whose constraints are convex. It is shown that this uncertain optimization problem can be approximated in a conservative manner by an uncertain linear optimization program, which enables the use of the techniques of robust linear programming of Ben-Tal, ElGhaoui, and Nemirovski [robust Optimization, Princeton University Press, 2009]. This methodology is then applied to two real cases of aircraft design and numerical results are presented.

关键词： robust linear programming optimization under uncertainty application to aircraft design

来源：评论

学校读者我要写书评

暂无评论

A Newton-Based Perturbation Method for a robust Inverse Optimization Problem

引用

Journal of Mathematical Research with Applications 2016年第6期36卷 741-753页

作者： Zhiqiang JIA Jian GU Xiantao XIAO School of Mathematical Sciences Dalian University of Technology School of Sciences Dalian Ocean University

In this paper,we aim to solve an inverse robust optimization problem,in which the parameters in both the objective function and the robust constraint set need to be adjusted as little as possible so that a known feasible solution becomes the optimal *** formulate this inverse problem as a minimization problem with a linear equality constraint,a second-order cone complementarity constraint and a linear complementarity constraint.A perturbation approach is constructed to solve the inverse *** inexact Newton method with Armijo line search is applied to solve the perturbed ***,the numerical results are reported to show the effectiveness of the approach.

关键词： inverse optimization robust linear programming perturbation approach inexact Newton method

来源：评论

学校读者我要写书评

暂无评论

A unifying framework for duality and modeling in robust linear programs

引用

OMEGA-INTERNATIONAL JOURNAL OF MANAGEMENT SCIENCE 2013年第6期41卷 984-997页

作者： Soyster, A. L. Murphy, F. H. Northeastern Univ Boston MA 02115 USA Temple Univ Fox Sch Business Philadelphia PA 19122 USA

In this paper, our major theme is a unifying framework for duality in robust linear programming. We show that there are two pair of dual programs allied with a robust linear program;one in which the primal is constructed to be "ultra-conservative" and one in which the primal is constructed to be "ultra-optimistic." Furthermore, as one would expect, if the uncertainly in the primal is row-based, the corresponding uncertainty in the dual is column-based, and vice-versa. Several examples are provided that illustrate the properties of these primal and dual models. A second theme of the paper is about modeling in robust linear programming. We replace the ordinary activity vectors (points) and right-hand sides with well-known geometric objects such as hyper-rectangles, parallel line segments and hyper-spheres. In this manner, imprecision and uncertainty can be explicitly modeled as an inherent characteristic of the model. This is in contrast to the usual approach of using vectors to model activities and/or constraints and then, subsequently, imposing some further constraints in the model to accommodate imprecision and uncertainties. The unifying duality structure is then applied to these models to understand and interpret the marginal prices. The key observation is that the optimal solutions to these dual problems are comprised of two parts: a traditional "centrality" component along with a "robustness" component. (C) 2012 Elsevier Ltd, All rights reserved.

关键词： robust linear programming Duality

来源：评论

学校读者我要写书评

暂无评论

robust stability and stabilization of uncertain linear positive systems via integral linear constraints: L₁-gain and L_∞-gain characterization

引用

INTERNATIONAL JOURNAL OF robust AND NONlinear CONTROL 2013年第17期23卷 1932-1954页

作者： Briat, Corentin Swiss Fed Inst Technol Zurich ETH Z Dept Biosyst Sci & Engn D BSSE CH-4058 Basel Switzerland KTH ACCESS Linnaeus Ctr Stockholm Sweden

Copositive linear Lyapunov functions are used along with dissipativity theory for stability analysis and control of uncertain linear positive systems. Unlike usual results on linear systems, linear supply rates are employed here for robustness and performance analysis using L-1-gain and L-gain. robust stability analysis is performed using integral linear constraints for which several classes of uncertainties are discussed. The approach is then extended to robust stabilization and performance optimization. The obtained results are expressed in terms of robust linear programming problems that are equivalently turned into finite dimensional ones using Handelman's theorem. Several examples are provided for illustration. Copyright (c) 2012 John Wiley & Sons, Ltd.

关键词： positive linear systems robustness integral linear constraints robust control robust linear programming relaxation

来源：评论

学校读者我要写书评

暂无评论

Two-stage robust LP with ellipsoidal right-hand side uncertainty is NP-hard

引用

OPTIMIZATION LETTERS 2012年第7期6卷 1463-1475页

作者： Minoux, Michel Univ Paris 06 F-75005 Paris France

As shown in previous work, robust linear programming problems featuring polyhedral right-hand side (RHS) uncertainty (a) arise in many practical applications;(b) frequently lead to robust equivalents belonging to the class of strongly NP-hard problems. In the present paper the case of ellipsoidal RHS uncertainty is investigated and similar complexity results are shown to hold even when restricting to simplified specially structured problems related to robust production planning under uncertain customer requirements. The proof is based on a reduction which significantly differs from the one used in the case of polyhedral RHS uncertainty.

关键词： robust optimization robust linear programming Polyhedral uncertainty Ellipsoidal uncertainty Complexity of robust linear 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：