Recent Advances and Historical Development of Vector Optimization: Proceedings of an International Conference on Vector Optimization Held at the Technical University of Darmstadt, FRG, August 4–7, 198

ISBN-13: 9783540182153 / Angielski / Miękka / 1987 / 405 str.

Johannes Jahn;Werner Krabs

Opis

In vector optimization one investigates optimization problems in an abstract setting which have a not necessarily real-valued objective function. This scientific discipline is closely related to multi-objective optimization and multi-criteria decision making. This book contains refereed contributions to the "International Conference on Vector Optimization" held at the Technical University of Darmstadt from August 4-7, 1986. This meeting was an interdisciplinary forum devoted to new results in the theory, to applications as well as to the solution of vector optimization problems which are relevant in practice. Because of the great variety of topics covered by the contributions, the 25 articles of this volume are organized in different sections: Historical retrospect, mathematical theory, goal setting and decision making, engineering applications, and related topics. The papers of the invited State-of-the-Art Tutorials given by Professors J.M. Borwein, H. Eschenauer, W. Stadler and P.L. Yu are also included.

Spis treści

I. Historical Retrospect.- Initiators of Multicriteria Optimization.- II. Mathematical Theory.- Well Posedness of Vector Optimization Problems.- Convex Cones, Minimality Notions, and Consequences.- Evaluation Functionals are the Extreme Points of a Basis for the Dual of C1+[a,b].- Polarities and Stability in Vector Optimization.- Sets of Efficiency in a Normed Space and Inner Product.- Recent Results on Duality in Vector Optimization.- A Result of Farkas Type and Duality in Vector Optimization.- Parametric Optimization with a Bottleneck Objective and Vector Optimization.- Duality in Partially Ordered Sets.- Generating Nested Subsets of Efficient Solutions.- Hierarchical Structures in Multicriteria Decision Making.- Well Posedness, Towards Vector Optimization.- On Some Applications of Stochastic Dominance in Multiobjective Decision-Making.- Some Considerations About Compùtational Complexity for Multi Objective Combinatorial Problems.- On the Existence of Cone-Efficient Points.- Pseudo-Utilities.- III. Goal Setting and Decision Making.- A Fuzzy Concept of Efficiency.- An Approach to Measuring Consistency of Preference Vector Derivations Using Least Square Distance.- Aggregation Procedures for Hierarchically Grouped Decision Attributes with Application to Control System Performance Evaluation.- A Flexible Model for Multi-Objective Optimization.- Foundation of Effective Goal Setting.- IV. Engineering Applications.- Multicriteria Optimization Procedures in Application on Structural Mechanics Systems.- V. Related Topics.- The Efficiency of a Method of Feasible Directions for Solving Variational Inequalities.- Bivariational Bounding Methods.