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This volume contains the Proceedings of the Sixth French-German
Conference on Optimization, which took place in June 1991 at
Lambrecht (PfaIz). About one hundred scientists, mainly from France
and Germany, but also from other european countries, met at the
Palatinate Conference Center in the heart of the beautiful
palatinate national park to review and discuss recent developments
in the field of optimization. More than sixty lectures were
delivered, covering a large part of the theoretical and practical
aspects of optimization. They all contributed to a stimulating
scientific exchange during the meeting. This conference was the
sixth in a series which started in 1980. Proceedings of the
previous French-German Conferences on Optimization have been
published as follows: First Conference (Oberwolfach 1980):
Optimization and Optimal Control, edited by A. Auslender, W. Oettli
and J. Stoer (Lecture Notes in Control and Information Sciences,
30). Springer Verlag, Berlin and Heidelber. e;, 1981 Second
Conference (Confolant, 1981): Optimization, edited by J. -B.
Hiriart-Urruty, W. Oettli, J. Stoer (Lecture Notes in Pure and
Applied Mathematics, 86). Marcel Dekker, New York and Basel1983
Third Conference (Lnminy, 1984): Third Franco-German Conference in
Optimization, edited by C. Lemarechal. Institut National de
Recherche en Informatique et en Automatique, Rocquencourt, 1984
(ISBN 2-7261-0402-9) Fourth Conference (Irsee, 1986): Trends in
Mathematical Optimization, edited by K. Hoffmann, J. -B.
Hiriart-Urruty, C. Lemarechal, J. Zowe (International Series of
Numerical Mathematics, 84). Birkhauser Verlag, Basel and Boston
1988 Fifth Conference (Varetz, 1988): Optimization, edited by S.
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Optimization, Parallel Processing and Applications - Proceedings of the Oberwolfach Conference on Operations Research, February 16-21, 1987 and the Workshop on Advanced Computation Techniques, Parallel Processing and Optimization Held at Karlsruhe, West Germany, February 22-25, 1987 (Paperback, Softcover reprint of the original 1st ed. 1988)
Alexander Kurzhanski, Klaus Neumann, Diethard Pallaschke
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R2,797
Discovery Miles 27 970
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It is already a tradition that conferences on operations research
are organized by the Mathematisches Forschungsinstitut in
Oberwolfach/Germany. The mean point of the 1987 conference was to
discuss recentl.v developed methods in optimization theory derived
from various fields of mathematics. On the other hand, the
practical use of results in operations research is very important.
In the last few years* essenti.al progress in this direction was
made at the International Insti- tute for Applied Systems Analysis
(IIASA) at Laxenburg/Austria. Therefore a three days workshop on
Advanced Computation Techniques, Parallel Processing and Optimi-
zation organized by IIASA and the University of Karlsruhe
immediately followed the Oberwolfach Conference. This volume
contains selected pape~s which have been presented at one of these
conferences. It:is divided into five sections based on the above
topics: I. Algorithms and Optimization Methods II. Optimization and
Parallel Processing III. Graph Theory and Scheduling IV.
Differential Equations and Operator Theory V. Applications. We
would like to thank the director of the Mathematisches
Forschungsinstitut Oberwolfach Prof. Dr. M. Barner and the
International Institute for Applied Systems Analysis, particularly
Prof. Dr. V. Kaftanov, and also to the director of the Computer
Center of the University of Karlsruhe Prof. Dr. A. Schreiner for
their support in organizing these conferences. We also appreciate
the excellent coopera- tion of Springer Verlag. We also thank Dr.
P. Recht, Dr. D. Solte and Dr. K. Wieder as well as*Mrs.
The International Institute for Applied Systems Analysis (IIASA) in
Laxenburg, Austria, has been involved in research on
nondifferentiable optimization since 1976. IIASA-based East-West
cooperation in this field has been very productive, leading to many
important theoretical, algorithmic and applied results.
Nondifferentiable optimi zation has now become a recognized and
rapidly developing branch of mathematical programming. To continue
this tradition, and to review recent developments in this field,
IIASA held a Workshop on Nondifferentiable Optimization in Sopron
(Hungary) in September 1964. The aims of the Workshop were: 1. To
discuss the state-of-the-art of nondifferentiable optimization
(NDO), its origins and motivation; 2. To compare-various
algorithms; 3. To evaluate existing mathematical approaches, their
applications and potential; 4. To extend and deepen industrial and
other applications of NDO. The following topics were considered in
separate sessions: General motivation for research in NDO:
nondifferentiability in applied problems, nondifferentiable
mathematical models. Numerical methods for solving
nondifferentiable optimization problems, numerical experiments,
comparisons and software. Nondifferentiable analysis: various
generalizations of the concept of subdifferen tials. Industrial and
other applications. This volume contains selected papers presented
at the Workshop. It is divided into four sections, based on the
above topics: I. Concepts in Nonsmooth Analysis II. Multicriteria
Optimization and Control Theory III. Algorithms and Optimization
Methods IV. Stochastic Programming and Applications We would like
to thank the International Institute for Applied Systems Analysis,
particularly Prof. V. Kaftanov and Prof. A.B. Kurzhanski, for their
support in organiz ing this meeting."
Let eRN be the usual vector-space of real N-uples with the usual
inner product denoted by (. ,. ). In this paper P is a nonempty
compact polyhedral set of mN, f is a real-valued function defined
on (RN continuously differentiable and fP is the line- ly
constrained minimization problem stated as : min (f(x) I x EURO P)
* For computing stationary points of problemtj) we propose a method
which attempts to operate within the linear-simplex method
structure. This method then appears as a same type of method as the
convex-simplex method of Zangwill [6]. It is however, different and
has the advantage of being less technical with regards to the
Zangwill method. It has also a simple geometrical interpretation
which makes it more under standable and more open to other
improvements. Also in the case where f is convex an implementable
line-search is proposed which is not the case in the Zangwill
method. Moreover, if f(x) = (c,x) this method will coincide with
the simplex method (this is also true in the case of the convex
simplex method) i if f(x) = I Ixl 12 it will be almost the same as
the algorithm given by Bazaraa, Goode, Rardin [2].
0.1. Grauert, H.; Lieb, I.: Differential- und Integralrechnung I.
Funktionen einer reel len Veranderlichen (Heidelberger Taschen-
bucher 26). 4. Aufl. Springer, Berlin - Heidelberg - New York 1976.
0.2. Grauert, H.; Fischer, w.: Differential- und Integralrechnung
II. Differentialrechnung in mehreren Veranderlichen. Differential-
gleichungen (Heidelberger Taschenbucher 36). 3. Aufl. Ebenfalls
1978. 0.3. Grauert, H.; Lieb, I.: Differential- und
Integralrechnunq III. Integrationstheorie. Kurven- und
Flachenintegrale (Heidelberger Taschenbuch 43). 2. Aufl. Ebenfalls
1977. 0.4. Janich, K.: Analysis fur Physiker und Ingenieure.
Springer, Berlin - Heidelberg - New York - Tokyo 1983. 0.5.
Kuratowski, K.: Introduction to Calculus (Pure and Appl. Math. 17).
Pergamon - Polish Scient. Publ., Oxford - London - New York- Paris
- Warszawa 1961 (Ubersetzung aus dem Polnischen) . 0.6. Sikorski,
R.: Advanced Calculus. Functions of Several Variables (Monogr. Mat.
51). Polish Scient. Publ., Warszawa 1969 (Ubersetzung aus dem
Polnischen) - 0.7. Strubecker, K.: Einfuhrung in die hahere
Mathematik mit beson- derer Berlicksichtigung ihrer Anwendungen auf
Geometrie, Physik, Naturwissenschaften und Technik, Band I:
Grundlagen. 2. Aufl. R. Oldenbourg, Munchen - \, lien 1966. 0.8.
Strubecker, K.: Einfuhrung in die hohere Mathematik --., Band II:
Differentialrechnung einer reellen Veranderlichen. Ebenfalls 1967.
0.9. Strubecker, K.: Einfuhrung in die hohere Mathematik -.-, Band
III: Integralrechnung einer reellen Veranderlichen. Ebenfalls 1980.
0.10. Wa ter, W.: Analysis I (Grundwiss. Math. 3). Springer,
Berlin- Heidelberg - New York - Tokyo 1984.
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