TY - JOUR

T1 - On the theory of non-linear minimax problems

AU - Dem’yanov, V. F.

AU - Malozemov, V. N.

N1 - Copyright: Copyright 2016 Elsevier B.V., All rights reserved.

PY - 1971/6/30

Y1 - 1971/6/30

N2 - This article is a survey of recent results on non-linear minimax problems. The following questions are considered: The directional differentiability of the maximum function;necessary conditions for a minimax and their geometrical interpretation; sufficient conditions for a local minimax; methods of successive approximation to find the stationary points of the maximum function; properties of the maximin function. These questions are set out first of all for the discrete case (Ch. I) and then for the general case (Ch. II); in the first chapter the accent is on methods of successive approximation, while in the second it is on the tie-up between the theory, as it has evolved, and certain classical results.

AB - This article is a survey of recent results on non-linear minimax problems. The following questions are considered: The directional differentiability of the maximum function;necessary conditions for a minimax and their geometrical interpretation; sufficient conditions for a local minimax; methods of successive approximation to find the stationary points of the maximum function; properties of the maximin function. These questions are set out first of all for the discrete case (Ch. I) and then for the general case (Ch. II); in the first chapter the accent is on methods of successive approximation, while in the second it is on the tie-up between the theory, as it has evolved, and certain classical results.

UR - http://www.scopus.com/inward/record.url?scp=0346417956&partnerID=8YFLogxK

U2 - 10.1070/RM1971v026n03ABEH003834

DO - 10.1070/RM1971v026n03ABEH003834

M3 - Article

AN - SCOPUS:0346417956

VL - 26

SP - 57

EP - 115

JO - Russian Mathematical Surveys

JF - Russian Mathematical Surveys

SN - 0036-0279

IS - 3

ER -