International Symposium on Systems Optimization and Analysis: Rocquencourt, December 11–13, 1978 IRIA LABORIA Institut de Recherche d'Informatique et d'Automatique Rocquencourt — France

339 Pages·1979·4.34 MB·English

by  M. A. Keyzer (auth.), Prof. A. Bensoussan, Prof. J. L. Lions (eds.)

Lecture Notes in
Control and
Information Sciences
Edited by A V Balakrishnan and M.Thoma
14
International Symposium on
Systems Optimization and
Analysis
Rocquencourt, December 11-13, 1978
IRIA LABORIA
Institut de Recherche d'lnformatique et d'Automatique
Rocquencourt - France
Edited by A. Bensoussan and J. L. Lions
Springer-Verlag
Berlin Heidelberg New York 1979
Series Editors
h~ V. Balakrishnan. M. Thoma
Advisory Board
L. D. Davisson • A. G. J. MacFarlane • H. Kwakernaak •
Ya. Z. Tsypkin
Editors
Prof. A. Bensoussan
Prof. J. L. Lions
IRIA LABORIA
Domaine de Voluceau - Rocquencourt
F-78150 Le ChesnaytFrance
With 16 Figures
ISBN 3-540-09447-4 Springer-Verlag Berlin Heidelberg NewYork
ISBN 0-387-0944?-4 Springer-Verlag NewYork Heidelberg Berlin
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© Springer-Verlag Berlin Heidelberg 1979
Printed in Germany
Printing and binding: Beltz Offsetdruck, Hemsbach/Bergstr.
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This symposium is organized by the Institut de Recherche d'Informatique et d'Automatique
under the sponsorship of:
• Association Fran~.aise pour la Cybern~tique Economique et Technique (AFCET)
• International Federation of Automatic Control (IFAC) Technical Committee of Theory
Ce colloque est organis6 par l'Institut de Recherche d'Informatlquee t d'Automatique( IRIA) sous le
patronage de:
• Association FranCalse pour la Cybern~tique Economique et Technique (AFCET)
• International Federation of Automatic (IFAC) Technical Committee of Theory
Organicers - Organisateurs
A. BENSOUSSAN
J. L. LIONS
Organization committee - Comit6 d'organisation
A. BENSOUSSAN
(IRIA/LABORIA)
P. FAURRE
(AFCET - IRIA/LABORIA)
A. FOSSARD
(AFCET)
H. KWAKERNAAK
(IFAC)
J. LESOURNE
(CNAM)
J. L. LIONS
(IRIA/LABORIA)
Scientific Secretaries - Secr6taires Scientifiques
P. NEPOMIASTCHY (IRIA/LABORIA)
Y. LEMARECHAL (IRIAJLABORIA)
Symposium Secretariat - Secr6tariat du Colloque
Th. BRICHETEAU (IPdM
Foreword
This international symposium on analysis and optimization was the
third of a series. Organized by IRIA with the co-sponsorship of AFCET
and IFAC, it has gathered more than 200 participants from 18 different
countries.
Five sessions were essentially dedicated to the following topics:
Economic models; identification, estimation, filtering; adaptative
control; numerical methods in optimization; distributed systems.
The conference was followed by a special two-day meeting on industrial
applications, co-organized by AFCET and IRIA. For this reason the
papers related with methodology were concentrated during the first
three days and will be found in this book.
The organizers wish to express their gratitude to IRIA for the support
given to the conference, in particular to the Department of External
Relations. Thanks should also be addressed to AFCET and IFAC for their
sponsorship.
This symposium is now regularly organized every two years in december.
The large variety of fields covered by "Analysis and Optimization"
allows the organizers to select and emphasize different topics at each
symposium.
The Springer-Verlag series "Lecture Notes in Control and Information
Sciences" edited by Professor Balakrishnan and Professor Thoma has
already published the proceedings of the second IRIA Symposium 1976.
We are quite happy to see the proceedings of the third one published
in the same series.
May, 1979 Alain Bensoussan Jacques-Louis Lions
Table of Contents - Table des matieres
ECONOMICAL MODELS
MODELES ~CONOMIQUES ............................................
An international agreement as a complementarity problem
M.A. Keyzer (Netherlands) ......................................
Solving nonlinear economic planning models using GRG
algorithms
L.S. La~don, A. Meerau~ (USA) .................................. 17
Specification and estimation of econometric models with
generalized expectations
K.D. Wall (USA) ................................................ 34
Implementation of the model in codes for control of large
econometric models
A. Drud (Denmark) ............................................... 49
MODULECO, aide ~ la construction et ~ l'utilisation de
modules macroe"c onomlques
P. Nepomiastchy, B. Oudet, F. Rechenmann (France) .............. 61
IDENTIFICATION, ESTIMATION, FILTERING
IDENTIFICATION, ESTIMATION, FILTRAGE ........................... 72
A calculus of multiparameter martingales and its
applications
E. Wong (USA) .................................................. 73
Orthogonal transformation (square root). Implementations of
the generalized Chandrasekhar and generalized Levinson
algorithms
f. KaiZath, A. Vieira, M. Morf (USA) ........................... 81
Shortest data description and consistency of order estimates
in arma-processes
J. Rissanen (USA) ..............................................
92
Spectral theory of linear control and estimation problems
E.A. Jonckheere, L.M. Silverman (USA) ..........................
9g
Un algorithme de lissage
M. CZerget, F. Germain (Prance) ................................ IiO
Reduced order modeling of closed-loop nash games
H.K. KhakiS, B.F. Gardner Jr., J.B. Cruz Jr.,
P.V. Kokotovie (USA) ............................................ 119
VII
Quantum estimation theory
S.K. Mitter, S.K. Young (USA) ................................. 127
ADAPTIVE CONTROL
CONTROLE ADAPTATIF ............................................ 137
Piece,wise deterministic signals
K.J. Astr~m (Sweden) .......................................... 138
Adaptive control of Markov chains
V. Borkar, P. Varaiya (USA) ................................... 145
Resource management in an automated warehouse
Y.C. Ho, R. Suri (USA) ........................................ 153
Dualit~ asymptotique entre les syst~mes de commande
adaptative avec mod&le et les r~gulateurs ~ variance
minimale auto-ajustables
Y. Landau (France) ............................................ 168
NUMERICAL METHODS IN OPTIMIZATION
MRTHODES NUMRRIQUES EN OPTIMISATION ........................... 178
On the Bertsekas' method for minimization of composite functions
B.T. PoZjak (USSR) ............................................ 179
On e-subgradient methods of non-differentiable
optimization
E.A. Nurminski (Austria) ..................................... 187
Non-differentiable optimization and large scale linear
programming
J.F. Shapiro (USA) ............................................ 196
Algorithms for non-linear multicommodity network flow
problems
D.P. Bertseka8 (USA) .......................................... 210
A 2-stage algorithm for minimax optimization
J. Hald, K. Madsen (Denmark) .................................. 225
DISTRIBUTED SYSTEMS
SYSTEMES DISTRIBUES ........................................... 240
Certain control problems in distributed systems
A.G. Butkovskiy (USSR) ........................................ 241
VIII
Partitioning: the multi-model framework for estimation
and control
D.G. Lainiotis (USA) ........................................... 252
Water waves and problems of infinite time control
D.L. Russel, R.M. Reid (USA) ................................... 291
Boundary stabilizability for diffusion processes
R. Triggiani (USA) ............................................. 304
Spline based approximation methods for control and
identification of hereditary systems
H.T. Banks, J.A. Burns, E.M. Cliff (USA) ....................... 314
Stabilization of boundary control systems
J. Zabczyk (Poland) ............................................ 321
ECONOMICAL MODELS
MODELES I~CONOMIQUES
AN INTERNATIONAL AGREEMENT AS A COMPLemENTARITY PROBLEM
M.A. Keyzer
Centre for World Food Studies
Free University, Amsterdam, the Netherlands
Abstract
A general equilibrium model is presented which describes
the operation of a buffer stock agreement on the world
market. The model is reformulated as a complementarity
problem and its solution through nonsmooth optimization
is described.
1. A COMPETITIVE MODEL
We consider an international economy as a system of commodity im-
porting - exporting nations who react to international prices. In such
an economy a competitive equilibrium can be defined as a system of
prices such that imports do not exceed exports for any commodity. We
take into consideration the full set of commodities the countries trade
in, thus following a general equilibrium approach as opposed to a part-
ial one. For each nation imports - exports are determined by a national
model. The possible structure of such a model will not be discussed in
this paper (cf. [6]).All that matters here is that the relation between
imports - exports and international prices is assumed to have the fol-
lowing characteristics, which closely follow the requirements set out
in Arrow and Hahn Ch. i [I].
(a) A national model is considered as a set of net demand functions of
world market prices. The functions are continuous for positive world
market prices.
For country h,h = I,...,L one has:
z h = z h (pW,kh), defined for pW ~ 0 (i.i)
W
p n-dimensional vector of world market prices
h
z n-dimensional vector of net demand by nation h
(net demand = demand - supply)
k h deficit on the balance of trade of nation h.
(b) National net demand is assumed to satisfy for all nonnegative world
market prices the following balance of trade equation:
pWzh = kh(pw ) 1 (1.2)
k h is the nation's deficit on the balance of trade; kh(pw) is con-
tinuous and homogeneous of degree one in pW. The deficits on the
balances of trade are distributed over countries in such a way that:
Z k h = 0 at all pW ~ 0 (1.3)
h
(c) Let d h be the nations vector of demand and yh the vector of supply
then by definition:
z h = d h - y h (1.4)
We assume that:
dh> 0 and yh> 0
o There exists a finite number c such that for i=l,..,n: y~ < C.
i
Price vectors are row vectors.
Quantity vectors are column vectors.