From Local to Global Optimization

347 Pages·2001·19.84 MB·English

by  J. B. Rosen, Peter Värbrand (eds.)

From Local to Global Optimization
N onconvex Optimization and Its Applications
Volume 53
Managing Editor:
Panos Pardalos
University of Florida, US.A.
Advisory Board:
l.R. Birge
Northwestern University, US.A.
Ding-Zhu Du
University of Minnesota, US.A.
C. A. Floudas
Princeton University, US.A.
1. Mockus
Lithuanian Academ.v of Sciences, Lithuania
H. D. Sherali
Virginia Polytechnic Institute and State University, US.A.
O. Stavroulakis
Technical University Braunschweig, Germany
The titles published in this series are listed at the end of this volume.
From Local to
Global Optimization
Edited by
Athanasios Migdalas
Technical University of Crete,
Chania, Crete, Greece
Panos M. Pardalos
University of Florida,
Gainesville, Florida, U.S.A.
and
Peter Varbrand
Linkoping University,
Norrkoping, Sweden
.....
SPRINGER-SCIENCE+BUSINESS MEDIA, B.V.
"
A c.I.P. Catalogue record for this book is available from the Library of Congress.
ISBN 978-1-4419-4852-6 ISBN 978-1-4757-5284-7 (eBook)
DOI 10.1007/978-1-4757-5284-7
Printed an acid-free paper
AII Rights Reserved
© 2001 Springer Science+Business Media Dordrecht
Originally published by Kluwer Academic Publishers in 2001
Softcover reprint of the hardcover 1s t edition 200 1
No part of the material protected by this copyright notice may be reproduced Of
utilized in any form or by any means, electronic or mechanical,
including photocopying, recording or by any information storage and
retrieval system, without written permission from the copyright owner.
Contents
Preface xv
xvii
Hoang Tuy: An Appreciation
1
1
Convex Global Underestimation for Molecular Structure Prediction
A. T. Phillips, J.B. Rosen, and K.A. Dill
1.1 Introduction 2
1.2 Overview of the CGU Search Method 3
1.3 Summary of Recent Results 4
1.4 Summary 14
References 15
2
19
Bayesian Heuristic Approach (BHA) and Applications to Discrete
Optimization
Jonas Mockus
2.1 Introduction 20
2.2 Knapsack Problem 22
2.3 Flow-Shop Problem 26
2.4 Batch Process Scheduling by MRP Heuristics 30
2.5 Computing Results 33
v
VI FROM LOCAL TO GLOBAL OPTIMIZATION
2.6 Software for Global Optimization 35
2.7 Dynamic Visualization in Modeling and Optimization of III
Defined Problems 38
References 45
3
49
A Finite Branch-and-Bound Method for Bilinear Hydro Power Scheduling
Stefan Feltenmark, P. O. Lindberg
3.1 Introduction 50
3.2 Problem statement 50
3.3 The branch-and-bound procedure 52
3.4 Finite termination 56
3.5 Computational results 61
3.6 Conclusions 65
References 67
4
69
Two Examples of Global Optimization by Means of Local Techniques
Antanas Zilinskas1
4.1 Introduction 70
4.2 Maximization of Throughput of Slotted ALOHA 71
4.3 Fast Local Descent Method for MDS 75
References 83
5
85
Modelling techniques for nonlinear pooling problems
Mikael Ronnqvist
Contents Vll
5.1 Introduction 85
5.2 A simple pooling problem 87
5.3 Refinery distillation 92
5.4 Modeling of nonlinear mixing 93
5.5 A case study 97
5.6 Concluding remarks 100
References 103
6
105
Optimization and Hierarchies for Lumped Distributed Networks
Alain Bui
6.1 Introduction 106
6.2 Preliminaries 106
6.3 Lumped networks and hierarchies based on optimization 112
6.4 Applications to some problems of distributed algorithms 115
References 131
7
133
n Tuy's 1964 Cone Splitting Algorithm for Concave Minimization
Christophe Meyer
7.1 Introduction 133
7.2 Basic operations 135
7.3 Algorithm 139
7.4 Examples 142
7.5 Conclusions 150
References 151
viii FROM LOCAL TO GLOBAL OPTIMIZATION
8
155
The aBB Global Optimization Algorithm for Nonconvex Problems:
An Overview
Claire S. Adjiman and Christodoulos A. Floudas1
8.1 Introduction 156
8.2 The aBB Global Optimization Algorithm 157
8.3 Computing the Diagonal Shift Matrix 161
8.4 Branching Variable Selection 169
8.5 Variable Bound Updates 171
8.6 Algorithm and Implementation 172
8.7 Computational Studies 174
8.8 Conclusions 182
References 183
9
187
Infimum of Polynomials and Singularity at Infinity
HA Huy Vui
9.1 Introduction 187
9.2 Statement of results 188
9.3 A method of complex geometry for finding infimum values 190
9.4 An example 191
9.5 Proofs 193
References 203
10
205
Solving Global Optimization Problems with BARON
Vinay Ghildyal1 and Nikolaos V. Sahinidis2
Contents IX
10.1 Introduction 206
10.2 Algorithms Used 207
10.3 System Features 217
10.4 Usage and Input/Output 224
10.5 Concluding Remarks 228
References 229
11
231
D.C. Programming Approach to the Multidimensional Scaling Problem
Le Thi Hoai An and Pham Dinh Tao
11.1 Introduction 232
11.2 D.c. optimization. 238
11.3 Lagrangian duality with zero gap in d.c. optimization. 246
11.4 Solving the Metric MDS Problem by DCA. 249
11.5 Normal Euclidean metric MDS as I?arametric trust region prob-
lem and solution by the parametnc DCA. 262
11.6 Computational experiments. 264
References 271
12
277
On Minimization of Sums of Heterogeneous Quadratic Functions
on Stiefel Manifolds.
T. Rapcsak1
12.1 Introduction 277
12.2 Optimization problem 278
12.3 Optimality conditions 281
12.4 Variable metric methods along geodesics 285
12.5 Proof of Theorem 4.1 286
x FROM LOCAL TO GLOBAL OPTIMIZATION
References 289
13
291
A Nonlinear Lagrangian FUnction for Discrete Optimization Problems
X.Q. Yang! and C.J. Goh
13.1 Introduction 291
13.2 A Nonlinear Lagrangian FUnction 293
13.3 Zero Duality Gaps 295
13.4 Applications 299
13.5 Conclusions 302
References 303
14
305
Local and Global Behavior of Moving Polytope Algorithms
Beidi Soumana Hamma
14.1 Introduction 305
14.2 Description of the algorithms 308
14.3 Preliminary Numerical Experiments 320
14.4 Conclusions 324
References 325
15
327
Relational Complementarity Problem
G. Isac1 , M. M. Kostreva2 , £3 M. Polyashukf
15.1 Introduction 328
15.2 Formulation 329
15.3 Relational complementarity problem. Existence of solutions 331