On the theory of non-linear minimax problems

Standard

On the theory of non-linear minimax problems. / Dem’yanov, V. F.; Malozemov, V. N.

In: Russian Mathematical Surveys, Vol. 26, No. 3, 30.06.1971, p. 57-115.

Research output: Contribution to journal › Article › peer-review

Author

Dem’yanov, V. F. ; Malozemov, V. N. / On the theory of non-linear minimax problems. In: Russian Mathematical Surveys. 1971 ; Vol. 26, No. 3. pp. 57-115.

BibTeX

@article{70f647e1138249d8982df6a572252ab5,

title = "On the theory of non-linear minimax problems",

abstract = "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.",

author = "Dem{\textquoteright}yanov, {V. F.} and Malozemov, {V. N.}",

year = "1971",

month = jun,

day = "30",

doi = "10.1070/RM1971v026n03ABEH003834",

language = "English",

volume = "26",

pages = "57--115",

journal = "Russian Mathematical Surveys",

issn = "0036-0279",

publisher = "IOP Publishing Ltd.",

number = "3",

}

RIS

TY - JOUR

T1 - On the theory of non-linear minimax problems

AU - Dem’yanov, V. F.

AU - Malozemov, V. N.

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 -

ID: 73932438