On the convex approximation of nonlinear inequalities
- 1 January 1974
- journal article
- research article
- Published by Taylor & Francis in Mathematische Operationsforschung und Statistik
- Vol. 5 (6) , 451-466
- https://doi.org/10.1080/02331887408801180
Abstract
The present paper deals with sufficient conditions for a system of convex incqualities to be a local approximation of a given arbitrary system in the following sense: the solution set of the first system is tangential to the solution set of the second one at the point under consideration. a criterion is proposed. For the case, in which the given system is of then form x ∈ D, H(x) ∈ N, where D is a subset of a certain linear topological space X, H a mapping from D into Rk , N a closed convex cone in R k . Form this eriterion an extremum principle is deduced, which contains as particular cases certain well-known results such as the clasical KUHN-TUCKER theorem, the Halkin's theorein [2], the Mangasarian-Fromowitz's theorem [3]. Some other results (containing a well-known theorem of Ljusternik [7]) are obtained in the case where H is a mapping from D into a Banach space Y.Keywords
This publication has 1 reference indexed in Scilit:
- An Abstract Variational Theory with Applications to a Broad Class of Optimization Problems. I. General TheorySIAM Journal on Control, 1966