Optimization and Optimal Control: Proceedings of a Conference Held at Oberwolfach, March 16–22, 1980

251 Pages·1981·4.169 MB·English

by  M. Atteia, A. El Qortobi (auth.), Alfred Auslender, Werner Oettli, Josef Stoer (eds.)

Lecture Notes ni
Control dna
noitamrofnI Sciences
Edited yb .V.A Balakrishnan dna M.Thoma
30
IIII II I I
noitazimitpO dna
lamitpO lortnoC
Proceedings of a Conference Held at
Oberwolfach, March 16-22, 1980
detidE by
.A Auslender, W. Oettli, and .J Stoer
IIII II IIIIIIIIIIIII IIIIIIIIIII HIIII I II
galreV-regnirpS
nilreB Heidelberg New kroY 1891
Series Editors
A, .V Balakrishnan • M. Thoma
Advisory Board
L D, Davisson A. • G..1. MacFarlane • H. Kwakernaak
.1, L Massey • .aY Z. Tsypkin • A, .J Viterbi
Editors
Alfred Auslender
D@partement de Math@matiques Appliqu~es
Universit@ de Clerrnont-Ferrand II
B.P. 45
07136-=1 Aubi@re (France)
Werner Oettli
Fakult~t f~ir Mathematik und Informatik
Universit#,t Mannheim
SchloB
D-6800 Mannheim
.tosef Stoer
Institut fiJr Angewandte Mathematik und Statistik
Universit~t W0rzburg
Am Hubland
D-8700 W~irzburg
AMS Subject Classifications :)0891( 49 BXX, 49 CXX, 49 DXX, 65 KXX,
90CXX, 90DXX, 93EXX
ISBN 3-540-10627-8 Springer-Verlag Berlin Heidelberg NewYork
ISBN 0-387-10627-8 Springer-Verlag NewYork Heidelberg Berlin
This work is subject to copyright. All rights are reserved, whether the whole
or part of the material is concerned, specifically those of translation, re-
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machine or similar means, and storage in data banks.
Under § 54 of the German Copyright Law where copies are made for other
than private use a fee is payable to 'Verwertungsgesellschaft Wort', Munich.
© Springer-Verlag Berlin Heidelberg 1891
Printed in Germany
Printing and binding: Beltz Offsetdruck, Hemsbach/Bergstr.
2061/3020-543210
ECAFERP
This volume constitutes the proceedings of a conference held March 16-22, 1980, at
sehcsitamehtaM Forschungsinstitut Oberwolfach. ehT purpose of this conference saw
to treat recent advances in general optimization theory sa well sa in problems of
optimal control, dna also to establish closer contacts between scientists, main-
ly from France dna ,ynamreG working in these fields. Included gnoma the topics were
wen results in nonlinear analysis, used to obtain general optimality conditions.
This more abstract approach saw detnemelpmoc by techniques using the specific struc-
ture of particular function spaces arising in optimal control problems. Also includ-
de weret he development dna evaluation of numerical methods for solving problems of
this kind.
ehT organizers gratefully acknowledge the generous support received yb Mathemati-
sehcs Forschungsinstitut Oberwolfach.
.A Auslender .W Oettli J. Stoer
TSIL F OSTNAPICITRAP
.M ,AIETTA U.E.R. Sciences, tnemetrap~D ed ,seuqitam~htaM 118, eur ed ,ennobraN
77013 Toulouse, ecnarF
.A ,REDNELSUA tnemetrap~D ed seuqitam~htaM Appliqu~es, Universit~ ed ,tnomrelC
.P.B ,54 07136 Aubi~re, ecnarF
.G.H ,KCOB Institut fur etdnawegnA kitamehtaM red Universit~t ,nnoB e~artsrelegeW 6,
0035-D nnoB
J. ,REGNINUARB sehcsitamehtaM Institut der Universit~t Stuttgart,
Pfaffenwaldring ,75 0007-D Stuttgart
J. ,KNILAPS-KNIRB Institut fur ehcsiremuN dnu Instrumentelle ,kitamehtaM
Universit~t ,retsnUM RoxelerstraBe ,46 0044-D retsnUM
.M ,ETAKORB Institut fur ,kitamehtaM UF Berlin, Arnimallee 2-6, 00OI-D Berlin 33
.L ,ZTALLOC Institut fur etdnawegnA ,kitamehtaM Universit~t ,grubmaH
eBartssednuB ,55 0002-D grubmaH 31
.F ,SUINOLOC Universit~t ,nemerB BibliothekstraBe, Postfach 033 ,044
0082-D nemerB 33
J.P. tnemetrap~ D,XIEZUORC ed seuqitam~htaM Appliqu~es, Universit~ ed ,tnomrelC
B.P. ,54 07136 Aubi~re, ecnarF
.U ,TDRAHKCE Institut fur etdnawegnA ,kitamehtaM Universit~t ,grubmaH
eBartssednuB ,55 0002-D 31 grubmaH
I. ,DNALEKE U.E.R. seuqitam~htaM ed la D~cision, Universit~ ed Paris IX,
57757 Paris ,61 xed~C ecnarF
J. ,ESHERF Institut fur etdnawegnA ,kitamehtaM Universit~t ,nnoB BeringstraBe 4-6,
0035-D nnoB
.K ,FFOHSALG Institut fur etdnawegnA ,kitamehtaM Universit~t ,grubmaH
eBartssednuB ,55 0002-D grubmaH 31
.B ,NALLOG sehcsitamehtaM Institut, Universit~t ,grubzrUW mA ,dnalbuH
0078-D grubzrUW
. M,LEHCSTURG Universit~t ,nnoB Institut fur snoitarepO ,hcraeseR eBartsessaN 2,
0035-D nnoB i
J. ,RENNIWG Fakult~t fur kitamehtaM dnu Informatik, Universit~t ,miehnnaK
edu~begranimeS A ,5 0086-D miehnnaM
. W,HCSUBKCAH sehcsitamehtaM Institut red Universit~t K~ln, latreyeW 86-90,
0005-D K~ln 14
J.B. ,YTURRU-TRAIRIH tnemetrap~D ed seuqitam~htaM Appliqu~es, Universit~ ed
,tnomrelC B.P. ,54 07136 Aubiare, ecnarF
.H.K ,NNAMFFOH UF Berlin, Institut fur ,kitamehtaM Arnimallee 2-6,
00OI-D Berlin 33
.W NAV ,EDETSNOH Institut fur etdnawegnA ,kitamehtaM Universit~t ,nnoB
eBartsrelegeW 6, 0035-D nnoB
.P ,DRAUH E1ectricit~ ed France, ,1 euneva ud lar~n~G ed Gaulle, 92141Clamart,
ecnarF
J.L. ED ,GNOJ der Onderafde]ing ,ednuksiW ehcsinhceT ,loohcsegoH P.O. xoB ,315
,nevohdniE ehT sdnalrehteN
.P ,LLAK Universit~t ZUrich, eBartsgrebnieW ,95 6008-HC ZUrich, Switzerland
.F ,LEPPAK II. sehcsitamehtaM Institut, Universit~t Graz, ElisabethstraBe ,11
0108 Graz, Austria
V
.W.H ,HCOLBONK sehcsitamehtaM Institut red Universit~t ,grubzrUW mA ,dnalbuH
0078-D grubzrUW
.,MNNAtFLHOK Institut fur etdnawegnA ,kitamehtaM Universit~t ,nnoB
eBartsrelegeW 6, 0035-D nnoB
.B ,ETROK Institut fur Operations ,hcraeseR Universit~t ,nnoB eBartsessaN 2,
0035-D nnoB 1
.P ,LOMSOK sehcsitamehtaM ,ranimeS Universit~t Kiel, eBartsnesuahslO 40-60,
0032-D Kiel I
.W ,SBARK hcierebhcaF HT,kitamehtaM ,tdatsmraD eBartsnetragBolhcS 7,
0016-D tdatsmraD
.D ,TFARK Institut fur kimanyD red ,emetsysgulF D-80310berpfaffenhofen
P.J. ,TNERUAL Institut National Polytechnique ed Grenoble, eniamoD Universitaire,
B.P. ,35 ,xedeC-elbonerG14083 ecnarF
,,LCAHCERAMEL I.N.R.I.A., ,truocneuqcoR B.P. 105, 05187 eL ,yansehC ecnarF
.F ,OIPMEL Lehrstuhl fur ,kitamehtaM Universit~t Bayreuth, Postfach ,8003
0858-D htueryaB
,H T.UORNEKCAM h~ierebhcaF kitamehtaM dnu Physik, Universit~t Bayreuth,
hcaftsoP 3008, 0858-D htueryaB
, I.KKSWONALAM smetsyS hcraeseR Institute, Polska aimedakA ,kuaN ul. aksleweN 6,
744-10 ,awazsraW dnaloP
.D ,YEHTNAM Lehrstuhl fur kitamehtaM VII, Universit~t ,miehnnaM 0086-D miehnnaM
.H ,RERUAM Institut fur ehcsiremuN dnu Instrumentelle ,kitamehtaM
Universit~t ,retsnUM RoxelerstraBe ,46 0044-D retsnUM
.E ,IKSNIMRUN IIASA, Schlo~platz I, Laxenburg, Austria
H.J. ,ELREBO UT MUnchen, Fachbereich Mathematik, ArcisstraBe 21, D-8000 nehcnUM 2
.W OETTLI, Lehrstuhl fur Mathematik VII, Universit~t Mannheim, D-6800 miehnnaM
.D ,EKHCSALLAP ,DMG SchloB Birlinghoven, D-5205 St. Augustin
J.P. ,TONEP Facult~ des Sciences, Avenue Philippon, 64000 Pau, France
.J.H ,HCSEP UT ,nehcnUM hcierebhcaF ,kitamehtaM ArcisstraBe ,12 0008-D nehcnUM 2
.G ,ARREIP E.N.S.M.A., ,02 eur emualliuG le ,ruodabuorT 43068 Poitiers, ecnarF
.K ,RETTIR sehcsitamehtaM Institut ,A Universit~t Stuttgart, Pfaffenwaldring ,75
0007-D Stuttgart 08
.M.S ,NOSNIBOR University of ,nisnocsiW 016 tunlaW Street, ,nosidaM IW 53706, ASU
oT.R ,RALLEFAKCOR University of ,notgnihsaW tnemtrapeD of ,scitamehtaM Seattle,
AW ,59189 ASU
.E ,SHCAS UT Berlin, Fachbereich ,kitamehtaM StraSe sed .71 Juni ,531
00OI-D Berlin 21
.S ,ELBIAHCS tnemtrapeD of Finance, University of Alberta, ,notnomdE
Alberta G6T ,1G2 adanaC
, .IKKSWOKTTIHCS Institut fur etdnawegnA kitamehtaM dnu Statistik red Universit~t
,grubzrUW mA Hubland, 0078-D grubzrUW
.E ,OTACIDEPS Istituto Universitario di ,omagreB Via Salvecchio, 00142 ,omagreB
Italy
.P ,ICCULLEPS Fachbereich ,kitamehtaM HT ,tdatsmraD eBartsnetragBolhcS 7,
0016-D tdatsmraD
J. ,REOTS Institut fur etdnawegnA kitamehtaM dnu Statistik red Universit~t
,grubzrUW mA ,dnalbuH 0078-D grubzrUW
lV
.H.K ,LLEW Institut fur re dkimanyD ,emetsysgulF 1308-D nefohneffafprebO
J. ,EWOZ Lehrstuh] fur etdnawegnA ,kitamehtaM Universit~t ,htueryaB hcaftsoP ,8003
0858-D htueryaB
ELBAT FO STNETNOC
Part I: Optimization ............................................................ 1
.M Atteia, A, El Qortobi
Quasi-Convex Duality ......................................................... 3
J.-P. Crouzeix
emoS Differentiability Properties of Quasiconvex Functions no ~n ......,..,.. 9
j. Gwinner
nO Optimality Conditions for Infinite Programs .............................. 12
J.-B. Hiriart-Urruty
Optimality Conditions for Discrete Nonlinear Norm-Approximation
smelborP .................................................................... 92
.P drauH
Feasible Variable Metric Method for Nonlinearly Constrained
smelborP .................................................................... 34
.B Korte, .R Schrader
A Note no Convergence Proofs for Shor-Khachian-Methods ...................... 15
.C lahc~rameL
A View of Line-Searches ..................................................... 95
E.A. Nurminski
q-Approximation dna Decomposition of Large-Scale Problems ................... 97
J.-P. Penot
nO the Existence of Lagrange Multipliers in Nonlinear
gnimmargorP in Spaces Banach ................................................ 98
.S Schaible, I. gnaZ
Convexifiable Pseudoconvex dna Strictly xevnocoduesP
C:-Functions (Extended Abstract) ........................................... 501
.K Schittkowski
Organization, Test, dna Performance of Optimization Programs ............... 901
.P Spellucci
Han's Method without Solving PQ ............................................ 321
Part 2: O~timal Control ....................................................... 341
.M Brokate
Necessary Optimality Conditions for Differential semaG
with Transition Surfaces ................................................... 541
.F Colonius
Regularization of Lagrange Multipliers for Time Delay
smetsyS with Fixed Final State ............................................. 361
VIII
.W Hackbusch
Numerical Solution of Linear dna Nonlinear Parabolic
Control Problems ........................................................... 971
.M Kohlmann
Survey on Existence Results in Nonlinear Optimal
Stochastic Control of Semimartingales ...................................... 781
.W Krabs
Time-Minimal Controllability in the View of Optimization ................... 112
.D Kraft
nO the Choice of Minimization Algorithms in Parametric
Optimal Control Problems ................................................... 912
,U Mackenroth
Strong Duality, kaeW Duality dna Penalization for a
State Constrained Parabolic Control Problem ................................ 332
.K Malanowski
Finite Difference Approximations to Constrained Optimal
Control Problems ........................................................... 342
Part :1
noitazimitpO