Singular optimal regimes in problems of mathematical economics
type: Item
instance of: scholarly article
title: Singular optimal regimes in problems of mathematical economics
zbMATH Open document ID: 1088.49022
author: M. I. Zelikin
author: V. F. Borisov
published in: Journal of Mathematical Sciences (New York)
publication date: 2006-01-23T00:00:00Z
review text: This paper consists of two chapters, focusing on singular extremals and their role in the construction of optimal syntheses. Economical interpretations are given for the results obtained. The approach in finding singular extremals is based on the method of differential forms. An optimality condition for finding singular extremals is proved, which is thought to be more effective than the results obtained via the classical calculus of variations. Theorems with applications in Economy, among which the attractor theorem for first-order singular regimes and various theorems on the structure of optimal synthesis in a neighborhood of singular regimes, are translated in the language of differential forms and then proved. The second chapter is devoted to second order singular trajectories and nonsingular extremals with accumulation of switchings. The authors introduce and discuss here basic concepts of switching accumulation regimes, such as the theorem on the existence of a bundle containing trajectories with switching accumulation, the theorem on the Lagrangian submanifold, sufficient optimality conditions for this regime, or the attractor theorem. The presentation is accompanied by many examples and problems, together with their detailed solutions.
Mathematics Subject Classification ID: 49K15
Mathematics Subject Classification ID: 49N60
Mathematics Subject Classification ID: 91B62
zbMATH DE Number: 5000638
zbMATH Keywords: optimal synthesis
zbMATH Keywords: singular regimes
zbMATH Keywords: switching accumulation regimes
reviewed by: Gheorghe Aniculăesei
MaRDI profile type: Publication
full work available at URL: s10958-005-0350-5
OpenAlex ID: W2084173668
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DOI: 10.1007/S10958-005-0350-5
description: scientific article; zbMATH DE number 5000638