Further generalization of the Dubovicki-Milutin theorem
type: Item
instance of: scholarly article
title: Further generalization of the Dubovicki-Milutin theorem
zbMATH Open document ID: 0597.49016
DOI: 10.1007/BF00940202
published in: Journal of Optimization Theory and Applications
publication date: 1987-01-01T00:00:00Z
review text: Combining the results of \textit{W. Walczak} [ibid. 42, 561-582 (1984; Zbl 0504.52001)] and \textit{I. Lasiecka} [ibid. 24, 421-436 (1978; Zbl 0351.49006) and ''Conical approximations of sets with application to optimization problems'', Ph.D. Thesis, Tech. Univ. Warsaw/Poland (1974)], we extend the well-known Dubovicki-Milutin theorem in two directions: (i) we allow for treatment of several equality constraints in optimization problems; and (ii) we assume less regularity of optimization problems by requiring the existence of external cones instead of tangent cones. An example of optimization problem is also considered.
Mathematics Subject Classification ID: 49K10
Mathematics Subject Classification ID: 52A20
Mathematics Subject Classification ID: 90C30
zbMATH DE Number: 3962584
zbMATH Keywords: Dubovicki-Milutin theorem
zbMATH Keywords: external cones
zbMATH Keywords: internal cones
author: Wiesław Kotarski
MaRDI profile type: Publication
cites work: Some properties of cones in normed spaces and their application to investigating extremal problems
cites work: Generalization of the Dubovitzky-Milutyn optimality conditions
cites work: Lectures on mathematical theory of extremum problems. Translated from the Russian by D. Louvish
description: scientific article; zbMATH DE number 3962584