Table Of ContentEditorial Board
D. Gries • P. Brinch Hansen • C. Moter • G. Seegmfiller • N. Wirth
Prof. Dr. R. Conti
Istituto di Matematica
"Ulisse Dini"
Universit5 di Firenze
Viale Morgagni 67/A
1-50134 Firenze/Italia
Prof. Dr. Antonio Ruberti
Istituto di Automatica
Universit5 di Roma
Via Eudossiana 18
1-00184 Roma/Italia
AMS Subject Classifications (1970): 49-02, 49A40, 49B20, 49B35, 49B40, 49C05, 49C10,
49DXX, 65K05, 68A25, 68A45, 90-02, 90C05, 90C10,
90C20, 90C30, 90C50, 90C99, 90D05, 90D25, 90D99,
93-02, 93B05, 93B10, 93B20, 93B30, 93B35, 93B99,
93C20, 93E05, 93E20
ISBN 3-540-06583-0 Springer-Verlag Berlin , Heidelberg ' New York
ISBN 0-387-06583-0 Springer-Verlag New York • Heidelberg - Berlin
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© by Springer-Verlag Berlin. Heidelberg i973. Library of Congress Catalog Card Number 73-20818. Printed in Germany.
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PREFACE
The s e P r o c e e d i n g s a r e based on the p a p e r s p r e s e n t e d at the 5th IF IP
C o n f e r e n c e on Op t imiza t ion T e c h n i q u e s held in R o m e , l~Iay 7-11, 1973. The
C o n f e r e n c e was s p o n s o r e d by the IF IP T e c h n i c a l C o m m i t t e e on Op t imiza t ion
(TC-7) and by the Cons ig l io Naz iona le de l l e R i c e r c h e (I ta l ian Nat ional R e s e a r c h
Council).
The Conference was devotedt o recent advances in optimization techniques
and their application to modelling, identification and control of large systems.
Major emphasis of the Conference was on the most recent application areas,
including: Environmental Systems, Soeio-economic SystemsB,i ological Systems.
An interesting feature of the Conference was the participation of specialists
both in control theory and in the field of application of systems engineering.
The Proceedings are divided into two volumes. In the first are collected
the papers in which the methodological aspects are emphasized; in the second
those dealing with various application areas.
The International Program Committee of the Conference consisted of:
R. Conti, A. Ruberti (Italy) Chairmen, Fe de Veubeke (Belgium), E. Goto (Japan),
W. J. Karplus (USA), J. L. Lions (France), G. Marehuk (USSR), C. Oleeh (Poland),
L. S. Pontryagin (USSR), E. Rofman (Argentina), J. Stoer (FRG), J.H. Westcott (UK).
Previously published optimization conferences:
Colloquium on Methods of Optimization. Held in Novosibirsk/USSR, June1 968.
(Lecture Notes in Mathematics, Vol. 112)
Symposium on Optimization. Held in Nice, June 1969.
(Lecture Notes in Mathematics, Vol. 132)
Computing Methods in Optimization Problems. Heldi n San Remo, September 1968.
(Lecture Notes in Operation Research and Mathematical Economics, Vol. 14)
TABLE OF CONTENTS
SYSTEM MODELLING AND IDENTIFICATION
Iden t i f ica t ion of S y s t e m s Subject to Random State D i s t u r b a n c e
A. V. B a l a k r i s h n a n . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
Adapt ive C o m p a r t i m e n t a l S t r u c t u r e s in Bio logy and Socie ty
R. R. Mohle r , W. D. Smith . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
On the Opt imal Size of Sys t em Model
M. Z. Dajani ................................................. 33
Information-theoretic Methods for Modelling and Analysing Large
Systems
R. E. Rink ................................................... 37
A New Criterion for Modelling Systems
L. W. Taylor, Jr ............................................. 46
Stochastic Extension and Functional Restrictionso f Ill-posed
Estimation Problems
E. Mosca ................................................... 57
Regression Operator in Infinite Dimensional Vector Spaces anIdt s
Application to Some Identification Problems
A. Szymanski ............................................... 69
An Approach to Identification and Optimization in Quality Control
W. Runggaldier, G.R. Jacur ................................... 83
On Optimal Estimation and Innovation Processes
Y. A. Rosanov ~
Identification de Domaines
J. Cea . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
The Model l ing of Ed ib le Oil Fa t Mix tu re s
J. O. Gray , J . A . A i n s l e y . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
103
DISTRIBUTED SYSTEMS
F r e e Boundary P r o b l e m s and Impu l se C o n t r o l
J. L. L ions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
116
A Convex P r o g r a m m i n g Method in H i l b e r t Space and Its App l i ca t ions
to Opt ima l C o n t r o l of S y s t e m s D e s c r i b e d by P a r a b o l i c Equa t ions
K. Malanowski . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
124
~paper not r e c e i v e d
VI
About Some Free Boundary Problems Connected with Hydraulics
C. Baiocchi ................................................. I 37
M4thode de D4composition Appliqu~e au Contr61e Optimal de
Systbmes Distribu4s
A. Bensoussan, R. Glowinski, J.L. Lions ....................... 14 !
Approximation of Optimal Control Problems of Systems Described
by Boundary-value Mixed Problems of Dirichlet-Neumann Type
P. Colli Franzone ............................................ ] 52
Control of Parabolic Systems with Boundary Conditions Involving Time-Delays
P. K. C. Wang ................................................ ] 65
GAME THEORY
Characterization of Cones of Functions Isomorphic to Cones of
Convex Functions
J. -P. Aubin ................................................. 174
Necessary Conditions anSdu fficient Conditions for Pareto Optimality
in a Multicriterion Perturbed System
J. -L. Goffin, A. Haurie ....................................... ] 84
A Unified Theory of Deterministic Two-Players Zero-Sum
Differential Games
C. Marchal .................................................. 194
About Optimality of Time of Pursuit
M. S. Nikol'skii ............................................... 202
PATTERN RECOGNITION
Algebraic Automata and Optimal Solutioinns Pattern Recognition
E. Astesiano, G. Costa ........................................ 206
A New Feature Selection Procedure for Pattern Recognition Based on
Supervised Learning
J. Kittler .................................................... 218
On Recognition of High Deformed Patterns by Meanso f Multilevel
Descriptions
S. T y s z k o ~ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
A Classification Problem in Medical Radioscintigraphy
G. Walch ...................................................... 250
The Dynamic Clusters Method and Optimizatioinn Non-Hierarchical
Clustering
E. Diday ..................................................... 241
~paper not received
Vll
OPTIMAL CONTROL
A M a x i m u m P r i n c i p l e f o r G e n e r a l C o n s t r a i n e d O p t i m a l C o n t r o l
P r o b l e m s - An E p s i l o n T e c h n i q u e A p p r o a c h
J . W. M e r s k y . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 259
Op t i m a l C o n t r o l of S y s t e m s G o v e r n e d by V a r i a t i o n a l I n e q u a l i t i e s
J . P . Yvon . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 265
On D e t e r m i n i n g the S u b m a n i f o l d s of S t a t e S p a c e W h e r e the O p t i m a l
V a l u e S u r f a c e H a s an I n f i n i t e D e r i v a t i v e
H. L. S t a l f o r d . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 276
Con t r o l of A f f i n e S y s t e m s wi th M e m o r y
M. C. D e l f o u r , S . K . M i t t e r . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 292
Com p u t a t i o n a l M e t h o d s in H i l b e r t S p a c e f o r O p t i m a l C o n t r o l P r o b l e m s
w i t h D e l a y s
A. P . W i e r z b i c k i , A. Ha tko . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 304
Su f f i c i e n t C o n d i t i o n s of O p t i m a l i t y f o r C o n t i n g e n t E q u a t i o n s
V. I. B l a g o d a t s k i h . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 319
Va r i a t i o n a l A p p r o x i m a t i o n s of S o m e O p t i m a l C o n t r o l P r o b l e m s
T. Z o l e z z i . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 329
Norm Perturbation o:[ Supremum Problems
J. Baranger ................................................ 333
On Two Conjectures about the Closed-Loop Time-Optimal Control
P . B r u n o v s k ~ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 341
Cou p l i n g of S t a t e V a r i a b l e s in t he O p t i m a l Low T h r u s t O r b i t a l
T r a n s f e r P r o b l e m
R. H e n r i o n . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 345
Op t i m i z a t i o n of the A m m o n i a O x i d a t i o n P r o c e s s U s e d in t he M a n u f a c t u r e
of N i t r i c A c i d
P . U r o n e n , E. K i u k a a n n i e m i . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 360
STOCHASTIC CONTROL
S t o c h a s t i c C o n t r o l wi th a t M o s t D e n u m e r a b l e N u m b e r of C o r r e c t i o n s
J. Z a b c z y k . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
370
De s i g n of O p t i m a l I n c o m p l e t e S t a t e F e e d b a c k C o n t r o l l e r s f o r L a r g e
L i n e a r C o n s t a n t S y s t e m s
W . J . N a e i j e , P . Va lk , O . H . B o s g r a . . . . . . . . . . . . . . . . . . . . . . . . . . . .
375
Con t r o l of a Non L i n e a r S t o c h a s t i c B o u n d a r y V a l u e P r o b l e m
J. P . K e r n e v e z , J . P . Q u a d r a t , M. V io t . . . . . . . . . . . . . . . . . . . . . . . . . 389
An A l g o r i t h m to E s t i m a t e S u b - O p t i m a l P r e s e n t V a l u e s f o r U n i c h a i n
M a r k o v P r o c e s s e s w i th A l t e r n a t i v e R e w a r d S t r u c t u r e s
S. D a s Gup ta . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
399
VIII
MAT H E M A T I C A L P R O G R A M M I N G
Some Recent Developments in Nonlinear Programming
G. Zoutendijk ................................................ 407
Penalty Methods and Augmented Lagrangiansi n Nonlinear Programming
R. T. Rockafellar ............................................. 4t8
On INF-Compaet Mathematical Programs
R. J. -B. Wets ................................................ 426
Nonconvex Quadratic Programs, Linear Complementarity Problems, and
Integer Linear Programs
F. Giannessi, E. Tomasin ..................................... 437
A Widely Convergent Minimization Algorithm with Quadratic Termination
Property
G. Treccani ................................................. 450
A Heuristic Approach to Combinatorial Optimization Problems
E. Biondi, P.C. Palermo ...................................... 460
A New Solution for the General Set Covering Problem
L. B. Kov~cs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 471
A Theoretical Prediction of the Input-Output Table
E. Klafszky .................................................. 484
An Improved Algorithm for Pseudo-Boolean Programming
S.Walukiewicz, L. SZomifiski, M. Faner ......................... 493
Numerical Algorithms for Global Extremum Search
J. Evtushenko ................................................ 505
NUMERICAL METHODS
Generalized Sequential Gradient-Restoration Algorith with Applications
to Problems with Bounded Control, BoundedSt ate, and Bounded Time-
Rate of the State
A. Miele, J.N. Damoulakis ~ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Gradient Techniques for Computation of Stationary Points
E. K. Blum ................................................... 509
Parameterization and Graphic Aiidn Gradient Methods
J. -P. Peltier ................................................. 517
Les Algorithmes de Coordination danlas M~thode Mixte d'Optimisation &
Deux Niveaux
G. Grateloup, A° Titli, T. Lef~vre .............................. 526
~paper not received
IX
Applications of Decomposition and Multi-Level Techniques to the
Optimization of Distributed Parameter Systems
Ph. Cambon, L. Le Letty ..................................... 538
Attempt to Solve a Combinatorial Problem in the Continuum by a Method
of Extension-Reduction
E. Spedicato, G. Tagliabue ....................................
554
