Please use this identifier to cite or link to this item: http://hdl.handle.net/10995/111259
Title: Probabilistic Solutions of Conditional Optimization Problems
Authors: Timofeeva, G. A.
Issue Date: 2020
Publisher: Krasovskii Institute of Mathematics and Mechanics
Krasovskii Institute of Mathematics and Mechanics UB RAS
Citation: Timofeeva G. A. Probabilistic Solutions of Conditional Optimization Problems / G. A. Timofeeva // Trudy Instituta Matematiki i Mekhaniki UrO RAN. — 2020. — Vol. 26. — Iss. 1. — P. 198-212.
Abstract: Optimization problems with random parameters are studied. The traditional approach to their solution consists in finding a deterministic solution satisfying a certain criterion: optimization of the expected value of the objective function, optimization of the probability of attaining a certain level, or optimization of the quantile. In this review paper, we consider a solution of a stochastic optimization problem in the form of a random vector (or a random set). This is a relatively new class of problems, which is called "probabilistic optimization problems." It is noted that the application of probabilistic solutions in problems with random parameters is justified in the cases of multiple decision makers. Probabilistic optimization problems arise, for example, in the analysis of multicriteria problems; in this case, the weight coefficients of the importance of criteria are regarded as a random vector. We consider important examples of economic-mathematical models, which are optimization problems with a large number of decision makers: the problem of optimal choice based on the consumer's preference function, the route selection problem based on the optimization of the generalized cost of the trip, and the securities portfolio problem with a distribution of the investors' risk tolerance. Mathematical statements of these problems are given in the form of problems of probabilistic optimization. Some properties of the constructed models are studied; in particular, the expected value of the probabilistic solution of an optimization problem is analyzed. © 2020 Krasovskii Institute of Mathematics and Mechanics. All rights reserved.
Keywords: CONSUMER CHOICE
LINEAR CONVOLUTION OF CRITERIA
MULTICRITERIA OPTIMIZATION
PREFERENCE FUNCTION
PROBABILISTIC OPTIMIZATION
PROBABILISTIC SOLUTION
ROUTE SELECTION
SECURITIES PORTFOLIO PROBLEM
STOCHASTIC OPTIMIZATION
URI: http://hdl.handle.net/10995/111259
Access: info:eu-repo/semantics/openAccess
SCOPUS ID: 85090525117
PURE ID: 12459234
ISSN: 0134-4889
Appears in Collections:Научные публикации, проиндексированные в SCOPUS и WoS CC

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