Recent Trends in Optimization Theory and Applications

483 Pages·1995·17.44 MB·English

by  Agarwal R.P. (ed.)

RECENT TRENDS IN
OPTIMIZATION THEORY
AND
APPLICATIONS
WORLD SCIENTIFIC SERIES IN APPLICABLE ANALYSIS
Editor
Ravi P. Agarwal (National University of Singapore)
Advisory Board
J. M. Ball (Heriot-Watt Univ.)
Shui-Nee Chow (Georgia Inst. Tech.)
R. P. Gilbert (Univ. Delaware)
P. J. van der Houwen (Stichting Math. Centrum)
Junji Kato (Tohoku Univ.)
V. Lakshmikantham (Florida Inst. Tech.)
Masatake Mori (Univ. Tokyo)
M. Z. Nashed (Univ. Delaware)
Wolfgang Walter {Univ. Karlsruhe)
Vol. 1: Recent Trends in Differential Equations
ed. Ft. P. Agarwal
Vol. 2: Contributions in Numerical Mathematics
ed. R. P. Agarwal
Vol. 3: Inequalities and Applications
ed. R. P. Agarwal
Vol. 4: Dynamical Systems and Applications
ed. R. P. Agarwal
Vol. 5: Recent Trends in Optimization Theory and Applications
ed. R. P. Agarwal
World Scientific Series in Applicable Analysis
Volume 5
Editor
R.P.Agarwal
Department of Mathematics
National University of Singapore
RECENT TRENDS IN
OPTIMIZATION THEORY
AND
APPLICATIONS
V fe World Scientific
1MT Singapore • New Jersey • London • Hong Kong
Published by
World Scientific Publishing Co. Pte. Ltd.
P O Box 128, Farrer Road, Singapore 9128
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British Library Cataloguing-in-Publication Data
A catalogue record for this book is available from the British Library.
RECENT TRENDS IN OPTIMIZATION THEORY AND APPLICATIONS
Copyright © 1995 by World Scientific Publishing Co. Pte. Ltd.
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Printed in Singapore by Uto-Print
V
Contributors
G.Leitmann (U.S.A.)
B.D.O.Anderson (Australia)
B-G Liu (P.R.China)
M.Bertaja (Italy)
J.Liu (U.S.A.)
O.J.Boxma (Holland)
Z-Q Luo (Canada)
O.Burdakov (France)
K.A.Lurie (U.S.A.)
A.Cantoni (Australia)
P.Maponi (Italy)
D.J.Clements (Australia)
J.B.Matson (Australia)
B.D.C/aven (Australia)
A.Mees (Australia)
J.B.Cruz, Jr. (U.S.A.)
G.Pacelli (Italy)
P.Diamond (Australia)
M.Pachter (U.S.A.)
S.V.Drakunov (U.S.A.)
I.Postlethwaite (U.K.)
Y.G.Evtushenko (Russia)
T.Rapcsak (Hungary)
N.M.Filatov (Germany)
M.C.Recchioni (Italy)
I.Galligani (Italy)
Y.Sakawa (Japan)
J.C.Geromel (Brazil)
S.V.Savastyuk (U.S.A.)
F.Giannessi (Italy)
K.Schittkowski (Germany)
M.J.Grimble (U.K.)
Y.Shi (U.S.A.)
G.O.Guardabassi (Italy)
M.A.Sikora (U.S.A.)
D-W Gu (U.K.)
D.D.Siljak (U.S.A.)
C.H.Houpis (U.S.A.)
K.L.Teo (Australia)
D.G.Hull (U.S.A.)
C.Tovey (Australia)
C.Itiki (U.S.A.)
P.Tseng (U.S.A.)
X.Jian (P.R.China)
F.E.Udwadia (U.S.A.)
M.A.Johnson (U.K.)
H.Unbehauen (Germany)
R.E.Kalaba (U.S.A.)
A.Vladimirov (Australia)
J.C.Kalkkuhl (U.K.)
B.Vo (Australia)
M.R.Katebi (U.K.)
J.F.Whidborne (U.K.)
T.J.Kim (U.S.A.)
R.Xu (U.S.A.)
P.Kloeden (Australia)
P.L.Yu (U.S.A.)
T.Kobylarz (U.S.A.)
V.G. Zhadan (Russia)
A.J.Laub (U.S.A.)
F.Zirilli (Italy)
C.S.Lee (Singapore)
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vii
Preface
World Scientific Series in Applicable Analysis (WSSIAA) aims at reporting
new developments of high mathematical standard and current interest. Each
volume in the series shall be devoted to the mathematical analysis that has
been applied or is potentially applicable to the solutions of scientific, engi­
neering, and social problems. This volume contains 30 research articles on
the theory of optimization and its applications by the leading scientists in the
field. It is hoped that the material in the present volume will open new vistas
in research. The editor is grateful to his colleague Sheng Qin for his help in
the preparation of this volume.
R.P.Agarwal
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ix
CONTENTS
Preface vii
Static Optimization of Queueing Systems 1
O. J. Boxma
On Properties of Newton's Method for Smooth and Nonsmooth
Equations 17
O. Burdakov
Relations between Invex Properties 25
B. D. Craven
Dual Cones in Spaces of Convex Sets and Fuzzy Sets 35
P. Diamond, A. Vladimirov and P. Kloeden
Dual Barrier-Projection Methods in Linear Programming 51
Y. G. Evtushenko and V. G. Zhadan
Solving Parameter Identification Problems on a Parallel-Vector
Computer 67
/. Galligani and M. Bertaja
Images, Separation of Sets and Extremum Problems 79
F. Giannessi and T. Rapcsdk
Parameter Estimation Under Distributed Constraints: Two Algorithms
for Convex Semi-Infinite Quadratic Programming Problems 107
G. O. Guardabassi, J. C. Geromel and X. Jian
Appell's Equations of Motion and the Generalized Inverse Form 123
C. Itiki, R. E. Kalaba and F. E. Udwadia
Plant Optimization and Performance Monitoring 145
M. A. Johnson and M. R. Katebi
Planning for the "Big One" 171
R. Kalaba and R. Xu
Dynamic Nonlinear Optimisation Using the Gate Function Approach 177
M. R. Katebi, J. C. Kalkkuhl and M. J. Grimble
X
Optimal Control Design Using Error Compensation 193
T. J. Kim and D. G. Hull
System Identification in Fuzzy Logic Control 207
T. Kobylarz, M. Pachter and C. H. Houpis
Control Strategies for an Endemic Disease in the Presence
of Uncertainty 221
C. S. Lee and G. Leitmann
On Second-Order Sufficient Conditions in Smooth Nonlinear
Programs 239
J. Liu and B.-G. Liu
Convergence Analysis of Primal-Dual Interior Point
Algorithms for Convex Quadratic Programs 255
Z.-Q. Luo
On Direct Relaxation of Optimal Material Design Problems for
Plates 271
K. A. Lurie
Upper and Lower Bounds in Quadratic Maximization With Integer
Constraints 297
P. Maponi, G. Pacelli, M. C. Recchioni and F. Zirilli
Riccati Difference Equations for Discrete Time Spectral Factorization
With Unit Circle Zeros 311
J. B. Matson, B. D. O. Anderson, A. J. Laub and D. J. Clements
On Global Convergence of an Algorithm for Optimal Control of
Discrete-Time Systems 327
Y. Sakawa
Optimal Decentralized Control for Stochastic Dynamic Systems 337
5. V. Savastyuk and D. D. Siljak
Parameter Estimation in Differential Equations 353
K. Schittkowski
Foundations of Designing Optimal Systems and Contingency Plans 371
Y. Shi and P. L. Yu