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Many books on optimization consider only finite dimensional spaces. This volume is unique in its emphasis: the first three chapters develop optimization in spaces without linear structure, and the analog of convex analysis is constructed for this case. Many new results have been proved specially for this publication. In the following chapters optimization in infinite topological and normed vector spaces is considered. The novelty consists in using the drop property for weak well-posedness of linear problems in Banach spaces and in a unified approach (by means of the Dolecki approximation) to necessary conditions of optimality. The method of reduction of constraints for sufficient conditions of optimality is presented. The book contains an introduction to non-differentiable and vector optimization. Audience: This volume will be of interest to mathematicians, engineers, and economists working in mathematical optimization.
This volume contains selected papers presented either at the Oberwolfach Conference on Operations Research, February 1987, or at the three-day workshop on Advanced Computation Techniques, Parallel Processing and Optimization organized by IIASA and the University of Karlsruhe, which immediately followed. The aim of the conferences was to discuss recently developed methods in optimization theory and their practical implementation using advanced computation techniques, especially in parallel processing. The volume is divided into five sections: I. Algorithms and Optimization Methods II. Optimization and Parallel Processing III. Graph Theory and Scheduling IV. Differential Equations and Operator Theory V. Applications.
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 € 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].
This voluume contains actual contributions to the current research directions in Optimizatiton Theory as well as applications to economic problems and to problems in industrial engineering. Of particular interest are: convex- and Nonsmooth Analysis, Sensitivity Theory, Optimization techniques for nonsmooth and Variational problems, Control Theory and Vector optimization. The volume contains research andsurvey papers. The main benefit is given by a global suruvey of the state ofart of modern Optimization Theory and some typical applications.
This volume presents state-of-the-art models, algorithms, and applications of quantitative methods in management and economics. The papers are clustered into four parts, focusing on optimization issues, applications of Operations Research in production and service management, applications of Operations Research in logistics, and interdisciplinary approaches.
Approach your problems from the right It isn't that they can't see the solution. end and begin with the answers. Then, It is that they can't see the problem. one day, perhaps you will find the final G.K. Chesterton, The Scandal of Fa question. ther Brown 'The point of a Pin'. 'The Hermit Clad in Crane Feathers' in R. Van Gulik's The Chinese Maze Murders. Growing specialization and diversification have brought a host of mono graphs and textbooks on increasingly specialized topics. However, the "tree" of knowledge of mathematics and related fields does not grow only by putting forth new branches. It also happens, quite often in fact, that branches which were thought to be completely disparate ...
2 Radiant sets 236 3 Co-radiant sets 239 4 Radiative and co-radiative sets 241 5 Radiant sets with Lipschitz continuous Minkowski gauges 245 6 Star-shaped sets and their kernels 249 7 Separation 251 8 Abstract convex star-shaped sets 255 References 260 11 DIFFERENCES OF CONVEX COMPACTA AND METRIC SPACES OF CON- 263 VEX COMPACTA WITH APPLICATIONS: A SURVEY A. M. Rubinov, A. A. Vladimirov 1 Introduction 264 2 Preliminaries 264 3 Differences of convex compact sets: general approach 266 4 Metric projections and corresponding differences (one-dimensional case) 267 5 The *-difference 269 6 The Demyanov difference 271 7 Geometric and inductive definitions of the D-difference 273 8 Applications to D...
This volume is the second of two volumes representing leading themes of current research in nonlinear analysis and optimization. The articles are written by prominent researchers in these two areas and bring the readers, advanced graduate students and researchers alike, to the frontline of the vigorous research in important fields of mathematics. This volume contains articles on optimization. Topics covered include the calculus of variations, constrained optimization problems, mathematical economics, metric regularity, nonsmooth analysis, optimal control, subdifferential calculus, time scales and transportation traffic. The companion volume (Contemporary Mathematics, Volume 513) is devoted t...
This book aims to further develop the theory of stochastic functional inclusions and their applications for describing the solutions of the initial and boundary value problems for partial differential inclusions. The self-contained volume is designed to introduce the reader in a systematic fashion, to new methods of the stochastic optimal control theory from the very beginning. The exposition contains detailed proofs and uses new and original methods to characterize the properties of stochastic functional inclusions that, up to the present time, have only been published recently by the author. The work is divided into seven chapters, with the first two acting as an introduction, containin...