Primal Lower Nice Functions and Their Moreau Envelopes

被引：9

作者：

Mazade, Marc ^{[1
]}

Thibault, Lionel ^{[1
]}

机构：

[1] Univ Montpellier 2, Pl Eugene Bataillon,Case Courrier 51, F-34095 Montpellier, France

来源：

COMPUTATIONAL AND ANALYTICAL MATHEMATICS: IN HONOR OF JONATHAN BORWEIN'S 60TH BIRTHDAY | 2013年 / 50卷

关键词：

Borwein-Preiss principle; Infimum convolution; Moreau envelopes; Primal lower nice functions; Proximal mappings; Semiconvex functions; Subdifferentials; PROX-REGULAR FUNCTIONS; HILBERT-SPACES; CONVEX-FUNCTIONS; BANACH-SPACES; SUBDIFFERENTIALS; INTEGRATION;

D O I：

10.1007/978-1-4614-7621-4_25

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

This paper studies two equivalent definitions of primal lower nice functions and some subdifferential characterizations of such functions. Various regularity properties of the associated Moreau envelopes and proximal mappings are also provided.

引用

页码：521 / 553

页数：33

共 27 条

[1] Bacak M, 2010, J CONVEX ANAL, V17, P737
[2] Integration of primal lower nice functions in Hilbert spaces
Bernard, F
Thibault, L
Zagrodny, D
[J]. JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, 2005, 124 (03) : 561 - 579
[3] Prox-regular functions in Hilbert spaces
Bernard, F
Thibault, L
[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2005, 303 (01) : 1 - 14
[4] Prox-regularity of functions and sets in Banach spaces
Bernard, F
Thibault, L
[J]. SET-VALUED ANALYSIS, 2004, 12 (1-2): : 25 - 47
[5] THE PROXIMAL NORMAL FORMULA IN BANACH-SPACE
BORWEIN, JM
GILES, JR
[J]. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1987, 302 (01) : 371 - 381
[6] Clarke F.H, 1983, OPTIMIZATION NONSMOO
[7] CORREA R, 1992, P AM MATH SOC, V116, P67
[8] Correa R, 1994, RECENT ADV NONSMOOTH, P18
[9] EVOLUTION-EQUATIONS WITH LACK OF CONVEXITY
DEGIOVANNI, M
MARINO, A
TOSQUES, M
[J]. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 1985, 9 (12) : 1401 - 1443
[10] NON-CONVEX MINIMIZATION PROBLEMS
EKELAND, I
[J]. BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY, 1979, 1 (03) : 443 - 474

← 1 2 3 →