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, 1986
Johannes Jahn, Werner Krabs
Springer, Dec 31, 1987 - Business & Economics - 405 pages
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.
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achieve algorithm analysis applied assumption attributes Banach Banach spaces Borwein bounded characterization co(A compact comparisons consider constraints continuous convergence convex cone convex set criteria criterion decision maker decision problems defined definition denoted dominance economics effective goal setting efficient points efficient solutions equations equivalent example exists feasible finite subset fuzzy given Hence implies inequality inner product space INPUT iteration lattice Lemma linear programming linear space lower semicontinuity Math mathematical matrix maximal method minimal element multicriteria optimization multifunction multiple objective neighborhood nondominated nonempty norm NP-complete objective function paper parameter Pareto Pareto-optimal partially ordered performance preference programming proof properly efficient properties Proposition quasi-ordering relation resp respect satisfied scalar sequence solution set solving structure Suppose theory tion topological sorting topological space topological vector space upper semicontinuity utility function values vector optimization problems weakly efficient Wierzbicki