Serafini P. (ed.) Mathematics of Multi Objective Optimization

Springer, 1985. — 437 p. — (International Centre for Mechanical Sciences, vol. 289). — ISBN: 978-3-211-81860-2.This volume colltains tbe proceedings of tbe seminar "Mathematics of Multi Objective Optimization" held at tbe International Centre for Mechanical Sciences, Udine, ltaly, during tbe week of September 3-4, 1984. The seminar aimed at reviewing the fundamental and most advanced mathematical issues in Multi Objective Optimization. This field bas been developed mainly in the last twenty years even if its origin can be traced back to Pareta 's work. The recent vigorous growth bas mainly consisted in a deeper understanding of the process of problem modelling and solving and in the development of many techniques to solve particular problems. However the investigation of the foundations of the subject has not developed at the same pace and a theoretical framework comparable to the one of scalar (i.e. one-objective) optimization is still missing. It was indeed the purpose of the seminar to review tbe mathematical apparatus underlying both the theory and the modelling of multi objective problems, in order to discuss and stimulate research on the basic mathematics of tbe field. The papers of this volume reflect this approach and therefore are not confined only to new original results, but they also try to report the most recent state of the art in each topic.
The contributions in the volume have been grouped in two parts: papers related to the theory and papers related to the modelling of multi objective problems. Then, within each part, the order of the contributions tries, whenever possible, to follow a path from the general to the particular with the minimum discontinuity between adjacent papers. The topics covered in the first part are: value functions both in a deterministic and in a stochastic setting, scalarization, duality, linear programming, dynamic programming and stability; the second part covers comparison of mathematical models, interactive decision making, weight assessment, scalarization models and applications (i.e. compromise and goa/programming, etc.).