检索结果-内蒙古大学图书馆

A superlinearly convergent QP-free algorithm for mathematical programs with equilibrium constraints

APPLIED MATHEMATICS AND COMPUTATION 2015年 269卷 885-903页

作者： Li, Jianling Huang, Renshuai Jian, Jinbao Guangxi Univ Coll Math & Informat Sci Nanning 530004 Guangxi Peoples R China Yulin Normal Univ Coll Math & Informat Sci Yulin 537000 Guangxi Peoples R China

In this paper, based on the smoothing techniques and the working set techniques, a QP-free algorithm for mathematical programs with equilibrium constraints (MPEC for short) is presented. Firstly, by Fischer-Burmeister function and smoothing techniques, the discussed problem is approximated by a smooth constrained optimization problem. Secondly, the working set, which is used to construct systems of linear equations, is generated by pivoting operation. At each iteration, the search direction is yielded by solving two or three systems of equations with the same coefficient matrix. Under mild conditions, the global convergence and superlinear convergence are shown. Moreover, we can conclude that the current iterative point is an exact stationary point of the discussed problem if the proposed algorithm stops after finite iterations. Finally, preliminary numerical results are reported. (C) 2015 Elsevier Inc. All rights reserved.

关键词： Equilibrium constraints mathematical programs QP-free algorithm Global convergence Superlinear convergence

来源：评论

学校读者我要写书评

暂无评论

Modeling mathematical programs with Equilibrium Constraints in Pyomo

Modeling Mathematical Programs with Equilibrium Constraints ...

引用

作者： Hart, W. E Siirola, J. D Sandia National Labs. Albuquerque NM.

We describe new capabilities for modeling MPEC problems within the Pyomo modeling software. These capabilities include new modeling components that represent complementarity conditions, modeling transformations for re-expressing models with complementarity conditions in other forms, and meta-solvers that apply transformations and numeric optimization solvers to optimize MPEC problems. We illustrate the breadth of Pyomo's modeling capabilities for MPEC problems, and we describe how Pyomo's meta-solvers can perform local and global optimization of MPEC problems.

关键词： mathematical programs Equilibrium constraints Pyomo Economic systems Algebraic modeling language mathematical programs with Equilibrium Constraint (MPEC)

来源：评论

学校读者我要写书评

暂无评论

Scheduling and resource allocation in wireless sensor networks

Scheduling and resource allocation in wireless sensor networ...

引用

作者： Alayev, Yosef City University of New York

学位级别：Ph.D.

In computer science and telecommunications, wireless sensor networks are an active research area. Each sensor in a wireless sensor network has some pre-defined or on demand tasks such as collecting or disseminating data. Network resources, such as broadcast channels, number of sensors, power, battery life, etc., are limited. Hence, a schedule is required to optimally allocate network resources so as to maximize some profit or minimize some cost. This thesis focuses on scheduling problems in the wireless sensor networks environment. In particular, we study three scheduling problems in the wireless sensor networks: broadcast scheduling, sensor scheduling for area monitoring, and content distribution scheduling. For each problem the goal is to find efficient scheduling algorithms that have good approximation guarantees and perform well in practice.

关键词： algorithms mathematical programs optimization resource allocation scheduling wireless sensor networks

来源：评论

学校读者我要写书评

暂无评论

A superlinearly convergent implicit smooth SQP algorithm for mathematical programs with nonlinear complementarity constraints

引用

COMPUTATIONAL OPTIMIZATION AND APPLICATIONS 2005年第3期31卷 335-361页

作者： Jian, JB Guangxi Univ Coll Math & Informat Sci Nanning 530004 Peoples R China

This paper discusses a special class of mathematical programs with nonlinear complementarity constraints, its goal is to present a globally and superlinearly convergent algorithm for the discussed problems. We first reformulate the complementarity constraints as a standard nonlinear equality and inequality constraints by making use of a class of generalized smoothing complementarity functions, then present a new SQP algorithm for the discussed problems. At each iteration, with the help of a pivoting operation, a master search direction is yielded by solving a quadratic program, and a correction search direction for avoiding the Maratos effect is generated by an explicit formula. Under suitable assumptions, without the strict complementarity on the upper-level inequality constraints, the proposed algorithm converges globally to a B-stationary point of the problems, and its convergence rate is superlinear.

关键词： nonlinear complementarity constraints mathematical programs SQP algorithm superlinear convergence

来源：评论

学校读者我要写书评

暂无评论

An active-set equality constrained Newton solver with feasibility restoration for inverse coefficient problems in elliptic variational inequalities

引用

INVERSE PROBLEMS 2008年第3期24卷 34017-1-34017-23页

作者： Hintermueller, M. Univ Sussex Dept Math Brighton E Sussex England

An output-least-squares formulation for a class of parameter identification problems for elliptic variational inequalities is considered. Based on the concept of C-stationarity an active set type solver with feasibility restoration is introduced. It is shown that the new method relates to the so-called implicit programming techniques in the context of mathematical programs with equilibrium constraints. In the discrete setting, in order to overcome the ill-posedness of the problem, the parameter of interest is discretized on a coarser mesh than the state of the system. In addition, if the parameter corresponds to the coefficient in the bilinear form of the underlying differential operator, an interior-point treatment is employed to maintain the coercivity of the elliptic operator. Moreover, the computational domain for the coefficient depends on the measurement data. The paper ends with a report on numerical tests including an application to a simplified lubrication problem in a rolling element device.

关键词： COMPLEMENTARITY CONSTRAINTS mathematical programs MINIMIZATION PROBLEMS OPTIMALITY

来源：评论

学校读者我要写书评

暂无评论

Using EPECs to model bilevel games in restructured electricity markets with locational prices

引用

OPERATIONS RESEARCH 2007年第5期55卷 809-827页

作者： Hu, Xinmin Ralph, Daniel Univ New S Wales Australian Sch Business Sydney NSW 2052 Australia Univ Cambridge Judge Business Sch Cambridge CB2 1AG England

We study a bilevel noncooperative game-theoretic model of restructured electricity markets, with locational marginal prices. Each player in this game faces a bilevel optimization problem that we model as a mathematical program with equilibrium constraints (MPEC). The corresponding game is an example of an equilibrium program with equilibrium constraints (EPEC). We establish sufficient conditions for the existence of pure-strategy Nash equilibria for this class of bilevel games and give some applications. We show by examples the effect of network transmission limits, i.e., congestion, on the existence of equilibria. Then we study, for more general equilibrium programs with equilibrium constraints, the weaker pure-strategy concepts of local Nash and Nash stationary equilibria. We pose the latter as solutions of complementarity problems (CPs) and show their equivalence with the former in some cases. Finally, we present numerical examples of methods that attempt to find local Nash equilibria or Nash stationary points of randomly generated electricity market games.

关键词： COMPLEMENTARITY CONSTRAINTS mathematical programs TRANSMISSION RIGHTS CONVERGENCE POWER EQUILIBRIA NETWORKS IMPLEMENTATION GENERATION OLIGOPOLY

来源：评论

学校读者我要写书评

暂无评论

Interior-point algorithms, penalty methods and equilibrium problems (vol 34, pg 155, 2006)

引用

COMPUTATIONAL OPTIMIZATION AND APPLICATIONS 2006年第2期35卷 281-281页

作者： Benson, Hande Y. Sen, Arun Shanno, David F. Vanderbei, Robert J. Decision Sciences Department LeBow College of Business Drexel University Philadelphia PA 19104 Department of Operation Research and Financial Engineering Princeton University Princeton NJ 08344 RUTCOR Rutgers Center of Operations Research Rutgers University New Brunswick NJ 08903

In this paper we consider the question of solving equilibriumproblems-formulated as complementarity problems and, more generally, mathematical programs withequilibrium constraints (MPECs)-as nonlinear programs, using an interior-point approach. Theseproblems pose theoretical difficulties for nonlinear solvers, including interior-point methods. Weexamine the use of penalty methods to get around these difficulties and provide substantialnumerical results. We go on to show that penalty methods can resolve some problems thatinterior-point algorithms encounter in general.

关键词： interior-point methods nonlinear programming penalty methods equilibriumproblems complementarity COMPLEMENTARITY CONSTRAINTS mathematical programs SQP ALGORITHM CONVERGENCE

来源：评论

学校读者我要写书评

暂无评论

A SQP Algorithm with Superlinear Convergence for Complementarity Constrainedly mathematical programs

A SQP Algorithm with Superlinear Convergence for Complementa...

引用

第四届运筹学及其应用国际研讨会

作者： Jin-Bao Jian Department of Mathematics and Information Guangxi University

＜正＞In this paper,a sequential quadratic programming（SQP） algorithm for solving a stationary point of a kind of mathematical programs with linear complementarity constraints is proposed,The algorithm is a modification of the SQP algoritm proposed by by Fukushima,Luo and Pang（Computational Optimization and Applications 10,5-34,1998.）,it is based on a reformulation of complementarity condition as a system of *** each iteration,to generate the search directions,one quadratic programming and one system of equations needed to be solved,a line and curve search is used to yield the step *** suitable as-sumptions, the algorithm is proved to possess global and superlinear convergence.

关键词： mathematical programs equilibrium constraints linear complementarity constraints SQP global convergence strong convergence superlinear convergence

来源：评论

学校读者我要写书评

暂无评论

mathematical programming models for characterizing dominance and potential optimality when multicriteria alternative values and weights are simultaneously incomplete

引用

IEEE TRANSACTIONS ON SYSTEMS MAN AND CYBERNETICS PART A-SYSTEMS AND HUMANS 2004年第5期34卷 601-614页

作者： Park, KS Univ Ulsan Coll Business Adm Ulsan 680749 South Korea

This paper is concerned with the use of incomplete information on both multicriteria alternative value scores and importance weights in evaluating decision alternatives under certainty. Two decision concepts-dominance and potential optimality (PO)-are employed to determine outperforming alternatives or acts. Given incomplete weights and exact value scores, it is known that the set of nondominated acts implies the set of potentially optimal acts. We here rediscover this set inclusive relation in a different and computationally efficient manner that develops a mixed-integer programming approach to dominance. When both value scores and weights are incomplete, we show that the set inclusive relation between dominance and PO may or may not hold. This is a result of how we define PO. Two different definitions of PO-weak PO and strong PO-are made in the sense that an act is weak potentially optimal when there exists at least one exact vector of value scores in the given incomplete value scores which render this act potentially optimal. An act is strong potentially optimal when this act is potentially optimal for all possible value scores. Less formally, this means that under the given incomplete information, weak PO stands for sometimes good while strong PO stands for always good, so we can thus say that the latter outperforms than the former. As a result, we show that the set of nondominated acts implies the set of strong potentially optimal acts. No certain set inclusive relationship exists between nondominated acts and weak potentially optimal acts. We also present computational aspects of establishing dominance, weak and strong PO, which include transformations of nonlinear problems into linear programming problems.

关键词： dominance incomplete preference information mathematical programs multicriteria decision analysis potential optimality (PO)

来源：评论

学校读者我要写书评

暂无评论

Optimization problems with equilibrium constraints and their numerical solution

引用

mathematical PROGRAMMING 2004年第1期101卷 119-149页

作者： Kocvara, M Outrata, JV Univ Erlangen Nurnberg Inst Appl Math D-91058 Erlangen Germany Acad Sci Czech Republ Inst Informat Theory & Automat CR-18208 Prague 8 Czech Republic

We consider a class of optimization problems with a generalized equation among the constraints. This class covers several problem types like MPEC (mathematical programs with Equilibrium Constraints) and MPCC (mathematical programs with Complementarity Constraints). We briefly review techniques used for numerical solution of these problems: penalty methods, nonlinear programming (NLP) techniques and Implicit Programming approach (ImP). We further present a new theoretical framework for the ImP technique that is particularly useful in case of difficult equilibria. Finally, three numerical examples are presented: an MPEC that can be solved by ImP but can hardly be formulated as a nonlinear program, an MPCC that cannot be solved by ImP and finally an MPEC solvable by both, ImP and NLP techniques. In the last example we compare the efficiency of the two approaches.

关键词： INTERIOR-POINT ALGORITHM mathematical programs COMPLEMENTARITY CONSTRAINTS GENERALIZED EQUATIONS EXACT PENALIZATION OPTIMALITY CONDITIONS NONSMOOTH STATIONARITY SYSTEMS

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：