检索结果-内蒙古大学图书馆

A parametric simplex algorithm for linear vector optimization problems

MATHEMATICAL PROGRAMMING 2017年第1-2期163卷 213-242页

作者： Rudloff, Birgit Ulus, Firdevs Vanderbei, Robert Vienna Univ Econ & Business Inst Stat & Math A-1020 Vienna Austria Bilkent Univ Dept Ind Engn TR-06800 Ankara Turkey Princeton Univ Dept Operat Res & Financial Engn Princeton NJ 08544 USA

In this paper, a parametric simplex algorithm for solving linear vector optimization problems (LVOPs) is presented. This algorithm can be seen as a variant of the multi-objective simplex (the Evans-Steuer) algorithm (Math Program 5(1):54-72, 1973). Different from it, the proposed algorithm works in the parameter space and does not aim to find the set of all efficient solutions. Instead, it finds a solution in the sense of Lohne (vector optimization with infimum and supremum. Springer, Berlin, 2011), that is, it finds a subset of efficient solutions that allows to generate the whole efficient frontier. In that sense, it can also be seen as a generalization of the parametric self-dual simplex algorithm, which originally is designed for solving single objective linear optimization problems, and is modified to solve two objective bounded LVOPs with the positive orthant as the ordering cone in RuszczyA"ski and Vanderbei (Econometrica 71(4):1287-1297, 2003). The algorithm proposed here works for any dimension, any solid pointed polyhedral ordering cone C and for bounded as well as unbounded problems. Numerical results are provided to compare the proposed algorithm with an objective space based LVOP algorithm [Benson's algorithm in Hamel et al. (J Global Optim 59(4):811-836, 2014)], that also provides a solution in the sense of Lohne (2011), and with the Evans-Steuer algorithm (1973). The results show that for non-degenerate problems the proposed algorithm outperforms Benson's algorithm and is on par with the Evans-Steuer algorithm. For highly degenerate problems Benson's algorithm (Hamel et al. 2014) outperforms the simplex-type algorithms;however, the parametric simplex algorithm is for these problems computationally much more efficient than the Evans-Steuer algorithm.

关键词： linear vector optimization Multiple objective optimization Algorithms Parameter space segmentation

来源：评论

学校读者我要写书评

暂无评论

An approach to duality via image space analysis and applications to linear vector optimization problems

引用

optimization 2024年第11期73卷 3437-3449页

作者： Yao, Chaoli Wang, Siqi Hainan Univ Sch Math & Stat Hainan Peoples R China

In Yao et al. [Yao CL, Wang SQ, Tammer C. Construction of vector-valued weak separation functions with applications to conjugate duality in vector optimization;2024. Submitted.], based on the idea of image space analysis and abstract convexity, we proposed a uniform framework of conjugate duality for the constrained vector optimization problems. This paper aims to apply this framework to linear vector optimizations. With the aid of a special collection of separation functions, a set-valued dual problem, which was also derived by Heyde, Lohne, Tammer in [Heyde F, Lohne A, Tammer C. The attainment of the solution of the dual program in vertices for vectorial linear programs. In: Barichard V, Ehrgott M, Gandibleux X, T'Kindt V, editors. Multiobjective programming and goal programming. 2009. p. 13-24. (Lecture Notes in Economics and Mathematical Systems;618).;Heyde F, Lohne A, Tammer C. Set-valued duality theory for multiple objective linear programs and application to mathematical finance. Math Meth Oper Res. 2009;69:159-179.], is obtained by this approach. Within the uniform framework, we provide a new way to construct this dual model, and to investigate the duality theory of it. In this method, the strong duality is established by the separation of sets in the image space and the generalized saddle points.

关键词： linear vector optimization image space analysis separation function conjugate duality

来源：评论

学校读者我要写书评

暂无评论

The Pascoletti-Serafini Scalarization Scheme and linear vector optimization

引用

JOURNAL OF optimization THEORY AND APPLICATIONS 2014年第2期162卷 559-576页

作者： Huong, N. T. T. Yen, N. D. Le Qui Don Univ Dept Informat Technol Hanoi Vietnam Vietnam Acad Sci & Technol Inst Math Hanoi 10307 Vietnam

The Pascoletti-Serafini scalarization scheme for general vector optimization problems is studied. It is specified to linear vector optimization to give minimal representation formulae for the weakly efficient solution set and the efficient solution set. Several facts on connectedness of the solution sets of Pascoletti-Serafini's scalar auxiliary problems, both for linear vector optimization and for nonlinear vector optimization, are established.

关键词： vector optimization linear vector optimization The Pascoletti-Serafini scalarization Representation formula Solution connectedness

来源：评论

学校读者我要写书评

暂无评论

The Adaptive Parameter Control Method and linear vector optimization

引用

VIETNAM JOURNAL OF MATHEMATICS 2015年第2期43卷 471-486页

作者： Huong, Nguyen Thi Thu Yen, Nguyen Dong Le Qui Don Univ Dept Informat Technol Hanoi Vietnam Vietnam Acad Sci & Technol Inst Math 18 Hoang Quoc Viet Hanoi 10307 Vietnam

The question of constructing a set of equidistant points, with a given small approximate distance, in the efficient and weakly efficient frontiers of a linear vector optimization problem of a general form, is considered in this paper. It is shown that the question can be solved by combining Pascoletti-Serafini's scalarization method (1984) and Eichfelder's adaptive parameter control method (2009) with a sensitivity analysis formula in linear programming, which was obtained by J. Gauvin (2001). Our investigation shows that one can avoid the strong second-order sufficient condition used by G. Eichfelder, which cannot be imposed on linear vector optimization problems.

关键词： vector optimization linear vector optimization Pascoletti-Serafini's scalarization method Eichfelder's adaptive parameter control method Sensitivity analysis in linear programming

来源：评论

学校读者我要写书评

暂无评论

A vector linear programming approach for certain global optimization problems

引用

JOURNAL OF GLOBAL optimization 2018年第2期72卷 347-372页

作者： Ciripoi, Daniel Loehne, Andreas Weissing, Benjamin Friedrich Schiller Univ Jena Dept Math D-07737 Jena Germany

Global optimization problems with a quasi-concave objective function and linear constraints are studied. We point out that various other classes of global optimization problems can be expressed in this way. We present two algorithms, which can be seen as slight modifications of Benson-type algorithms for multiple objective linear programs (MOLP). The modification of the MOLP algorithms results in a more efficient treatment of the studied optimization problems. This paper generalizes results of Schulz and Mittal (Math Program 141(1-2): 103-120, 2013) on quasi-concave problems and Shao and Ehrgott (optimization 65(2): 415-431, 2016) on multiplicative linear programs. Furthermore, it improves results of Lohne and Wagner (J Glob Optim 69(2): 369-385, 2017) on minimizing the difference f = g-h of two convex functions g, h where either g or h is polyhedral. Numerical examples are given and the results are compared with the global optimization software BARON.

关键词： Global optimization DC programming Multiobjective linear programming linear vector optimization

来源：评论

学校读者我要写书评

暂无评论

The vector linear program solver Bensolve - notes on theoretical background

引用

EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2017年第3期260卷 807-813页

作者： Loehne, Andreas Weissing, Benjamin Friedrich Schiller Univ Jena Dept Math D-07737 Jena Germany Martin Luther Univ Halle Wittenberg Dept Math Halle Saale Germany

Bensolve is an open source implementation of Benson's algorithm and its dual variant. Both algorithms compute primal and dual solutions of vector linear programs (VLP), which include the subclass of multiple objective linear programs (MOLP). The recent version of Bensolve can treat arbitrary vector linear programs whose upper image does not contain lines. This article surveys the theoretical background of the implementation. In particular, the role of VLP duality for the implementation is pointed out. Some numerical examples are provided. In contrast to the existing literature we consider a less restrictive class of vector linear programs. (C) 2016 Elsevier B.V. All rights reserved.

关键词： vector linear programming linear vector optimization Multi objective optimization

来源：评论

学校读者我要写书评

暂无评论

Solving DC programs with a polyhedral component utilizing a multiple objective linear programming solver

引用

JOURNAL OF GLOBAL optimization 2017年第2期69卷 369-385页

作者： Loehne, Andreas Wagner, Andrea Friedrich Schiller Univ Jena Dept Math D-07737 Jena Germany Vienna Univ Econ & Business Inst Stat & Math A-1020 Vienna Austria

A class of non-convex optimization problems with DC objective function is studied, where DC stands for being representable as the difference of two convex functions g and h. In particular, we deal with the special case where one of the two convex functions g or h is polyhedral. In case g is polyhedral, we show that a solution of the DC program can be obtained from a solution of an associated polyhedral projection problem. In case h is polyhedral, we prove that a solution of the DC program can be obtained by solving a polyhedral projection problem and finitely many convex programs. Since polyhedral projection is equivalent to multiple objective linear programming (MOLP), a MOLP solver (in the second case together with a convex programming solver) can be used to solve instances of DC programs with polyhedral component. Numerical examples are provided, among them an application to locational analysis.

关键词： DC programming Global optimization Polyhedral projection Multiple objective linear programming linear vector optimization

来源：评论

学校读者我要写书评

暂无评论

Solving polyhedral d.c. optimization problems via concave minimization

引用

JOURNAL OF GLOBAL optimization 2020年第1期78卷 37-47页

作者： vom Dahl, Simeon Loehne, Andreas Univ Paris Sud Dept Math F-91400 Orsay France Friedrich Schiller Univ Jena Dept Math D-07737 Jena Germany

The problem of minimizing the difference of two convex functions is called polyhedral d.c. optimization problem if at least one of the two component functions is polyhedral. We characterize the existence of global optimal solutions of polyhedral d.c. optimization problems. This result is used to show that, whenever the existence of an optimal solution can be certified, polyhedral d.c. optimization problems can be solved by certain concave minimization algorithms. No further assumptions are necessary in case of the first component being polyhedral and just some mild assumptions to the first component are required for the case where the second component is polyhedral. In case of both component functions being polyhedral, we obtain a primal and dual existence test and a primal and dual solution procedure. Numerical examples are discussed.

关键词： Global optimization D c programming Multi-objective linear programming linear vector optimization

来源：评论

学校读者我要写书评

暂无评论

Equivalence between polyhedral projection, multiple objective linear programming and vector linear programming

引用

MATHEMATICAL METHODS OF OPERATIONS RESEARCH 2016年第2期84卷 411-426页

作者： Loehne, Andreas Weissing, Benjamin Friedrich Schiller Univ Jena Dept Math D-07737 Jena Germany

Let a polyhedral convex set be given by a finite number of linear inequalities and consider the problem to project this set onto a subspace. This problem, called polyhedral projection problem, is shown to be equivalent to multiple objective linear programming. The number of objectives of the multiple objective linear program is by one higher than the dimension of the projected polyhedron. The result implies that an arbitrary vector linear program (with arbitrary polyhedral ordering cone) can be solved by solving a multiple objective linear program (i.e. a vector linear program with the standard ordering cone) with one additional objective space dimension.

关键词： vector linear programming linear vector optimization Multi-objective optimization Irredundant solution Representation of polyhedra

来源：评论

学校读者我要写书评

暂无评论

Computing the recession cone of a convex upper image via convex projection

引用

JOURNAL OF GLOBAL optimization 2024年第4期89卷 975-994页

作者： Kovacova, Gabriela Ulus, Firdevs Univ Calif Los Angeles Dept Math Los Angeles CA 90095 USA Bilkent Univ Dept Ind Engn TR-06800 Ankara Turkiye

It is possible to solve unbounded convex vector optimization problems (CVOPs) in two phases: (1) computing or approximating the recession cone of the upper image and (2) solving the equivalent bounded CVOP where the ordering cone is extended based on the first phase. In this paper, we consider unbounded CVOPs and propose an alternative solution methodology to compute or approximate the recession cone of the upper image. In particular, we relate the dual of the recession cone with the Lagrange dual of weighted sum scalarization problems whenever the dual problem can be written explicitly. Computing this set requires solving a convex (or polyhedral) projection problem. We show that this methodology can be applied to semidefinite, quadratic, and linear vector optimization problems and provide some numerical examples.

关键词： Convex vector optimization linear vector optimization Unbounded vector optimization Recession cone Convex projection

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：