检索结果-内蒙古大学图书馆

cutting plane algorithms for robust conic convex optimization problems

OPTIMIZATION METHODS & SOFTWARE 2006年第5期21卷 779-803页

作者： Gomez, J. A. Gomez, W. Univ Concepcion Dept Ingn Matemat Concepcion Chile Univ La Frontera Dept Ingn Matemat Temuco Chile

In this paper, we study some well-known cases of nonlinear programming problems, presenting them as instances of inexact or semi-infinite linear programming. The class of problems considered contains, in particular, semi-definite programming, second-order cone programming and special cases of inexact semi-definite programming. Strong duality results for the nonlinear problems studied are obtained via the Lagrangian duality. Using these results, we propose some dual algorithms for the studied classes of problems. The proposed algorithms can be interpreted as cutting plane or discretization algorithms. Finally, some comments on the convergence of the proposed algorithms and on preliminary numerical tests are given.

关键词： semi-infinite linear programming cutting plane algorithms conic programming

来源：评论

学校读者我要写书评

暂无评论

GENERALIZED FRACTIONAL-PROGRAMMING AND cutting plane algorithms

引用

JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS 1995年第1期87卷 103-120页

作者： BARROS, AI FRENK, JBG ERASMUS UNIV ROTTERDAM INST ECONOMETR3000 DR ROTTERDAMNETHERLANDS

In this paper, we introduce a variant of a cutting plane algorithm and show that this algorithm reduces to the well-known Dinkelbach-type procedure of Crouzeix, Ferland, and Schaible if the optimization problem is a generalized fractional program. By this observation, an easy geometrical interpretation of one of the most important algorithms in generalized fractional programming is obtained. Moreover, it is shown that the convergence of the Dinkelbach-type procedure is a direct consequence of the properties of this cutting plane method. Finally, a class of generalized fractional programs is considered where the standard positivity assumption on the denominators of the ratios of the objective function has to be imposed explicitly. It is also shown that, when using a Dinkelbach-type approach for this class of programs, the constraints ensuring the positivity on the denominators can be dropped.

关键词： GENERALIZED FRACTIONAL PROGRAMMING BOUNDEDLY LOWER SUBDIFFERENTIABLE FUNCTIONS cutting plane algorithms

来源：评论

学校读者我要写书评

暂无评论

On global optimality conditions and cutting plane algorithms

引用

JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS 2003年第1期118卷 201-216页

作者： Tuy, H Natl Ctr Nat Sci & Technol Math Inst Hanoi Vietnam

We discuss global optimality conditions and cutting plane algorithms for DC optimization. The discussion is motivated by certain incorrect results that have appeared recently in the literature on these topics. Incidentally, we investigate the relation of the Tikhonov reciprocity theorem to the optimality conditions for general nonconvex global optimization problems and show how the outer-approximation scheme developed earlier for DC programming can be used to solve a wider class of problems.

关键词： global optimization DC programming optimality conditions cutting plane algorithms

来源：评论

学校读者我要写书评

暂无评论

Analysis of some cutting plane algorithms of integer programming

Analysis of some cutting plane algorithms of integer program...

引用

10th IEEE International Scientific and Technical Conference on Dynamics of Systems, Mechanisms and Machines (Dynamics)

作者： Kolokolov, Alexander A. Zaozerskaya, Lidia A. Russian Acad Sci Sobolev Inst Math Siberian Branch Omsk Russia

ISBN: (纸本)9781509040490

Discrete optimization models and methods, in particular, the apparatus of integer programming, are often used for solving and analysis of many decision-making problems in computers design, productions planning and management, information technologies, engineering. In this paper we investigate some cutting plane algorithms for solving the set packing problem, which has a lot of applications in the mentioned above areas. We give previously obtained estimates on the number of iterations (cutting planes) of these algorithms. We study one class of the problems with random input data. This paper presents an original method for construction of families of set packing problems, which are polynomially solvable on average. Upper bounds on the average iterations number for the problems of these families are built.

关键词： discrete optimization integer programming set packing problem regular partitions cutting plane algorithms

来源：评论

学校读者我要写书评

暂无评论

THE MINIMIZATION OF LOWER SUBDIFFERENTIABLE FUNCTIONS UNDER NONLINEAR CONSTRAINTS - AN ALL FEASIBLE cutting plane ALGORITHM

引用

JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS 1988年第3期57卷 463-484页

作者： PLASTRIA, F 1.Centrum voor Statistiek en Operationeel Onderzoek Vrije Universiteit Brussel Brussels Belgium

Nonlinear, possibly nonsmooth, minimization problems are considered with boundedly lower subdifferentiable objective and constraints. An algorithm of the cutting plane type is developed, which has the property that the objective needs to be considered at feasible points only. It generates automatically a nondecreasing sequence of lower bounds converging to the optimal function value, thus admitting a rational rule for stopping the calculations when sufficient precision in the objective value has been obtained. Details are given concerning the efficient implementation of the algorithm. Computational results are reported concerning the algorithm as applied to continuous location problems with distance constraints.

关键词： Nonsmooth optimization boundedly lower subifferentiable functions cutting plane algorithms continuous location problems distance constraints

来源：评论

学校读者我要写书评

暂无评论

On the relation between the extended supporting hyperplane algorithm and Kelley's cutting plane algorithm

引用

JOURNAL OF GLOBAL OPTIMIZATION 2020年第1期78卷 161-179页

作者： Serrano, Felipe Schwarz, Robert Gleixner, Ambros Zuse Inst Berlin Dept Math Optimizat Takustr 7 D-14195 Berlin Germany

Recently, Kronqvist et al. (J Global Optim 64(2):249-272, 2016) rediscovered the supporting hyperplane algorithm of Veinott (Oper Res 15(1):147-152, 1967) and demonstrated its computational benefits for solving convex mixed integer nonlinear programs. In this paper we derive the algorithm from a geometric point of view. This enables us to show that the supporting hyperplane algorithm is equivalent to Kelley's cutting plane algorithm (J Soc Ind Appl Math 8(4):703-712, 1960) applied to a particular reformulation of the problem. As a result, we extend the applicability of the supporting hyperplane algorithm to convex problems represented by a class of general, not necessarily convex nor differentiable, functions.

关键词： Convex MINLP cutting plane algorithms Supporting hyperplane algorithm Nonsmooth Optimization

来源：评论

学校读者我要写书评

暂无评论

A sequential cutting plane algorithm for solving convex NLP problems

引用

EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2006年第2期173卷 444-464页

作者： Still, Claus Westerlund, Tapio Abo Akad Univ Dept Math FIN-20500 Turku Finland Abo Akad Univ Proc Design Lab FIN-20500 Turku Finland

In this paper we look at a new algorithm for solving convex nonlinear programming optimization problems. The algorithm is a cutting plane-based method, where the sizes of the subproblems remain fixed, thus avoiding the issue with constantly growing subproblems we have for the classical Kelley's cutting plane algorithm. Initial numerical experiments indicate that the algorithm is considerably faster than Kelley's cutting plane algorithm and also competitive with existing nonlinear programming algorithms. (c) 2005 Elsevier B.V. All rights reserved.

关键词： convex programming nonlinear programming cutting plane algorithms sequential linear programming

来源：评论

学校读者我要写书评

暂无评论

A cutting plane algorithm for graph coloring

引用

DISCRETE APPLIED MATHEMATICS 2008年第2期156卷 159-179页

作者： Mendez-Diaz, Isabel Zabala, Paula Univ Buenos Aires FCEyN Dept Computac RA-1053 Buenos Aires DF Argentina

We present an approach based on integer programming formulations of the graph coloring problem. Our goal is to develop models that remove some symmetrical solutions obtained by color permutations. We study the problem from a polyhedral point of view and determine some families of facets of the 0/1-polytope associated with one of these integer programming formulations. The theoretical results described here are used to design an efficient cutting plane algorithm. (C) 2007 Elsevier B.V. All rights reserved.

关键词： graph coloring integer programming facets of polyhedra cutting plane algorithms

来源：评论

学校读者我要写书评

暂无评论

Solving convex MINLP optimization problems using a sequential cutting plane algorithm

引用

COMPUTATIONAL OPTIMIZATION AND APPLICATIONS 2006年第1期34卷 63-83页

作者： Still, C Westerlund, T Abo Akad Univ Dept Math FIN-20500 Turku Finland Abo Akad Univ Proc Design Lab FIN-20500 Turku Finland

In this article we look at a new algorithm for solving convex mixed integer nonlinear programming problems. The algorithm uses an integrated approach, where a branch and bound strategy is mixed with solving nonlinear programming problems at each node of the tree. The nonlinear programming problems, at each node, are not solved to optimality, rather one iteration step is taken at each node and then branching is applied. A Sequential cutting plane (SCP) algorithm is used for solving the nonlinear programming problems by solving a sequence of linear programming problems. The proposed algorithm generates explicit lower bounds for the nodes in the branch and bound tree, which is a significant improvement over previous algorithms based on QP techniques. Initial numerical results indicate that the described algorithm is a competitive alternative to other existing algorithms for these types of problems.

关键词： convex programming branch and bound cutting plane algorithms mixed integer nonlinear programming

来源：评论

学校读者我要写书评

暂无评论

A cutting plane algorithm for the site layout planning problem with travel barriers

引用

COMPUTERS & OPERATIONS RESEARCH 2017年 82卷 36-51页

作者： Hammad, Ahmed W. A. Rey, David Akbarnezhad, Ali Univ New S Wales Sch Civil & Environm Engn Newcastle NSW Australia

Site layout planning is an imperative procedure that may significantly impact the productivity and the efficiency of logistical operations undertaken on a construction site. This paper considers the site layout planning problem (SLPP) which entails the allocation of temporary facilities on a construction site in the presence of travel barriers such that the total transportation cost between facilities is minimised. In order to account for travel barriers, the SLPP is typically solved under the assumption that the available region for facility layout can be discretised. In this paper, we propose a general Mixed Integer Programming (MIP) model to represent the SLPP, accounting for the presence of barriers, and we show how space-discretised formulations can be derived from this model. In particular, we propose a novel MIP model, which permits facilities to cover multiple locations. This is then benchmarked against a commonly adopted MIP model in the literature. We also highlight a systematic procedure to convert the continuous feasible space in SLPP to a set of discretised locations based on the concept of d-visibility, enabling us to approximate the barrier distance function embedded in the objective function. In particular, we focus on presenting a simple space discretisation approach for converting the continuous SLP into a discrete problem for which the discrete SLP models would be applicable. Space-discretised MIP formulations are highly combinatorial and we introduce a cutting plane algorithm to improve their tractability. Specifically, we propose a novel exact location-decomposition algorithm which works from a relaxed MIP formulation and iteratively generates feasibility cuts to converge to an optimal solution. Both space-discretised MIP models and the decomposition algorithm are tested on a large group of instances to analyse their effectiveness in solving the SLPP. Computational results indicate that the proposed location-decomposition algorithm improves on t

关键词： Site layout planning Mixed integer programming cutting plane algorithms Decomposition methods Global optimisation d-visibility

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：