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A nonlinear Lagrangian based on Fischer-Burmeister NCP function

APPLIED MATHEMATICS AND COMPUTATION 2007年第2期188卷 1344-1363页

作者： Ren, Yong-Hong Zhang, Li-Wei Xiao, Xian-Tao Liaoning Normal Univ Sch Math Dalian 116029 Peoples R China Dalian Univ Technol Dept Appl Math Dalian 116024 Peoples R China

This paper proposes a nonlinear Lagrangian Based on Fischer-Burmeister NCP function for solving nonlinear programming problems with inequality constraints. The convergence theorem shows that the sequence of points generated by this nonlinear Lagrange algorithm is locally convergent when the penalty parameter is less than a threshold under a set of suitable conditions on problem functions, and the error bound of solution, depending on the penalty parameter, is also established. Moreover, the paper develops the dual approach associated with the proposed nonlinear Lagrangian, in which the related duality theorem is demonstrated. Furthermore, it is shown that the condition number of the nonlinear Lagrangian Hessian at the optimal solution is proportional to the controlling penalty parameter. Numerical results for solving several nonlinear programming problems are reported, showing that the new nonlinear Lagrangian is superior over other known nonlinear Lagrangians for solving some nonlinear programming problems. (c) 2006 Elsevier Inc. All rights reserved.

关键词： nonlinear Lagrangian Fischer-Burmeister NCP function augmented Lagrangian dual algorithm condition number dual function

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A revised dual projective pivot algorithm for linear programming

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SIAM JOURNAL ON OPTIMIZATION 2005年第1期16卷 49-68页

作者： Pan, PQ Southeast Univ Dept Math Nanjing 210096 Peoples R China

We revise the dual projective pivot algorithm using sparse rectangular LU factors. In each iteration, the proposed algorithm solves at most three triangular systems, while simplex algorithms solve four. Instead of the classical basis, it uses a so-called pseudobasis ( a rectangular matrix having fewer columns than rows), thereby solving smaller linear systems with a potentially improved stability compared to simplex algorithms. Most importantly, it generates good search directions at a low cost. We report encouraging computational results on a set of 50 Netlib standard test problems as well as a set of 15 much larger real-world problems. A code named RDPPA 1.10 based on the proposed algorithm outperformed MINOS 5.51 significantly in terms of both iterations and run time. In particular, it appears that a high proportion of degenerate iterations need not imply many total iterations ( contradicting the common belief).

关键词： large-scale linear programming dual algorithm projection pivot pseudobasis deficient basis LU factorization

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Exponential-RED: A stabilizing AQM scheme for low- and high-speed TCP protocols

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IEEE-ACM TRANSACTIONS ON NETWORKING 2005年第5期13卷 1068-1081页

作者： Liu, S Basar, T Srikant, R Univ Illinois Dept Elect & Comp Engn Urbana IL 61801 USA Univ Illinois Coordinated Sci Lab Urbana IL 61801 USA

This paper introduces and analyzes a decentralized network congestion control algorithm which has dynamic adaptations at both user ends and link ends, a so-called general primal-dual algorithm. We obtain sufficient conditions for local stability of this algorithm in a general topology network with heterogeneous round-trip delays. Then, as an implementation of this algorithm in the Internet, we introduce an AQM (Active Queue Management) scheme called Exponential-RED (E-RED), which outperforms RED and is inherently stable when combined with TCP-Reno or its variants for high-speed networks.

关键词： congestion control dual algorithm primal algorithm primal-dual algorithm RED TCP

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A dual projective pivot algorithm for linear programming

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COMPUTATIONAL OPTIMIZATION AND APPLICATIONS 2004年第3期29卷 333-346页

作者： Pan, PQ SE Univ Dept Math Nanjing 210018 Peoples R China

Recently, a linear programming problem solver, called dual projective simplex method, was proposed (Pan, Computers and Mathematics with Applications, vol. 35, no. 6, pp. 119-135, 1998). This algorithm requires a crash procedure to provide an initial (normal or deficient) basis. In this paper, it is recast in a more compact form so that it can get itself started from scratch with any dual (basic or nonbasic) feasible solution. A new dual Phase-1 approach for producing such a solution is proposed. Reported are also computational results obtained with a set of standard NETLIB problems.

关键词： linear programming dual algorithm pseudo-basis pivot projection

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Modelling incentives for collaboration in mobile ad hoc networks

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PERFORMANCE EVALUATION 2004年第4期57卷 427-439页

作者： Crowcroft, J Gibbens, R Kelly, F Östring, S Univ Cambridge Comp Lab Cambridge CB2 3QG England Univ Cambridge Stat Lab Cambridge CB2 1SB England

This paper explores a model for the operation of an ad hoc mobile network. The model incorporates incentives for users to act as transit nodes on multi-hop paths and to be rewarded with their own ability to send traffic. The paper explores consequences of the model by means of fluid-level simulations of a network and illustrates the way in which network resources are allocated to users according to their geographical position. (C) 2004 Elsevier B.V. All rights reserved.

关键词： ad hoc mobile networks fluid-level simulations dual algorithm incentives

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Modelling incentives for collaboration in mobile ad hoc networks

Modelling incentives for collaboration in mobile ad hoc netw...

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1st Workshop in Modeling and Optimization of Mobile, Ad Hoc and Wireless Networks (WiOpt 03)

作者： Crowcroft, J Gibbens, R Kelly, F Östring, S Univ Cambridge Comp Lab Cambridge CB2 3QG England Univ Cambridge Stat Lab Cambridge CB2 1SB England

关键词： ad hoc mobile networks fluid-level simulations dual algorithm incentives

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A generalized dual phase-2 simplex algorithm

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2003年第1期149卷 1-16页

作者： Maros, I Univ London Imperial Coll Sci Technol & Med Dept Comp London SW7 2BZ England

Recently, the dual simplex method has attracted considerable interest. This is mostly due to its important role in solving mixed integer linear programming problems where dual feasible bases are readily available. Even more than that, it is a realistic alternative to the primal simplex method in many cases. Real world linear programming problems include all types of variables and constraints. This necessitates a version of the dual simplex algorithm that can handle all types of variables efficiently. The paper presents increasingly more capable dual algorithms that evolve into one which is based on the piecewise linear nature of the dual objective function. The distinguishing features of this method are: (i) in one iteration it can make progress equivalent to many traditional dual iterations, (ii) using proper data structures it can be implemented very efficiently so that an iteration requires hardly more work than the traditional pivot method, (iii) its effectiveness just increases if more upper bounded variables are present, (iv) it has inherently better numerical stability because it can create a large flexibility in finding a pivot element, (v) it can excel itself in coping with degeneracy as it can bypass dual degenerate vertices more easily than the traditional pivot procedures. The power of the method is demonstrated through examples. The performance on some real world problems is also presented. (C) 2002 Elsevier Science B.V. All rights reserved.

关键词： linear programming simplex method dual algorithm large scale optimization

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Controlling the Internet: A survey and some new results

Controlling the Internet: A survey and some new results

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42nd IEEE Conference on Decision and Control

作者： Liu, S Basar, T Srikant, R Univ Illinois Dept Elect & Comp Engn Urbana IL 61801 USA

ISBN: (纸本)0780379241

In the last few years, significant progress has been made in the mathematical modelling of congestion control and congestion feedback mechanisms in the Internet. The resulting models have proved to be very useful in improving existing control and feedback mechanisms, and to make them scalable to networks that operate at very high speeds. Tools from convex optimization, control theory and stochastic processes have played a major role in the development of this Internet congestion control theory. In this paper, we focus on the control-theoretic aspects of the theory, and review some recent developments in the design of stable, scalable congestion control mechanisms. We also present a new scheme that can improve the performance of the Internet with minimal changes to the current architecture.

关键词： AQM AVQ Congestion Control dual algorithm Generalized Nyquist Criterion Primal algorithm Primal-dual algorithm RED TCP

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On the Wagner-Whitin lot-sizing polyhedron

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MATHEMATICS OF OPERATIONS RESEARCH 2001年第3期26卷 591-600页

作者： Pereira, O Wolsey, L Univ Catholique Louvain FNRS DICE FSA B-1348 Louvain Belgium Univ Catholique Louvain CORE B-1348 Louvain Belgium Univ Catholique Louvain INMA B-1348 Louvain Belgium

We study a family of unbounded polyhedra arising in the study of uncapacitated lot-sizing problems with Wagner-Whitin costs. We present a new proof of integrality based on completely characterizing the bounded faces of maximal dimension, and in particular showing that they are integral. With n the number of periods, we derive an O(n(2)) algorithm to express any point within the polyhedron as a convex combination of extreme points and extreme rays. We also study adjacency on the polyhedra, and give a simple O(n) test for adjacency. Finally we observe that for a given objective function the face of optimal solutions can be found in O(n(2)).

关键词： polyhedra proof of integrality adjacency maximal faces dual algorithm lot-sizing Wagner-Whitin costs

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On the use of optimization models for portfolio selection. A review and some computational results

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Computational Economics 1994年第4期7卷 227-227页

作者： Pardalos, Panos M. Sandstroem, Mattias Zopounidis, Costas Department of Industrial and Systems Engineering University of Florida Gainesville USA Department of Computer Science Royal Institute of Technology (KTH) Stockholm Sweden Department of Production Engineering and Management Technical University of Crete Chania Crete Greece

Portfolio theory deals with the question of how to allocate resources among several competing alternatives (stocks, bonds), many of which have an unknown outcome. In this paper we provide an overview of different portfolio models with emphasis on the corresponding optimization problems. For the classical Markowitz mean-variance model we present computational results, applying a dual algorithm for constrained optimization.

关键词： bond portfolio optimization constraint optimization dual algorithm Portfolio selection

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