A role of lower semicontinuous functions in the combinatorial complexity of geometric problems

AbstractWe provide vector analogues of the classical interpolation theorems for lower semicontinuous functions due to Dowker and to Hahn and Katetov-Tong.

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Some characterizations of error bound for non-lower semicontinuous functions

Journal of Inequalities and Applications ◽

10.1186/s13660-019-1987-9 ◽

2019 ◽

Vol 2019 (1) ◽

Author(s):

Miantao Chao ◽

Xiuping Wang ◽

Dongying Liang

Keyword(s):

Error Bound ◽

Lower Semicontinuous ◽

Lower Semicontinuous Functions ◽

Semicontinuous Functions

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Minimax principles for lower semicontinuous functions and applications to nonlinear boundary value problems

Annales de l Institut Henri Poincaré C Analyse non linéaire ◽

10.1016/s0294-1449(16)30389-4 ◽

1986 ◽

Vol 3 (2) ◽

pp. 77-109 ◽

Cited By ~ 178

Author(s):

Andrzej Szulkin

Keyword(s):

Boundary Value Problems ◽

Nonlinear Boundary ◽

Lower Semicontinuous ◽

Boundary Value ◽

Nonlinear Boundary Value Problems ◽

Lower Semicontinuous Functions ◽

Nonlinear Boundary Value ◽

Semicontinuous Functions

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Error bounds for systems of lower semicontinuous functions in Asplund spaces

Mathematical Programming ◽

10.1007/s10107-007-0121-9 ◽

2007 ◽

Vol 116 (1-2) ◽

pp. 397-427 ◽

Cited By ~ 50

Author(s):

Huynh van Ngai ◽

Michel Théra

Keyword(s):

Error Bounds ◽

Lower Semicontinuous ◽

Lower Semicontinuous Functions ◽

Asplund Spaces ◽

Semicontinuous Functions

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Mean value property and subdifferential criteria for lower semicontinuous functions

Transactions of the American Mathematical Society ◽

10.1090/s0002-9947-1995-1307998-0 ◽

1995 ◽

Vol 347 (10) ◽

pp. 4147-4161 ◽

Cited By ~ 49

Author(s):

Didier Aussel ◽

Jean-Noël Corvellec ◽

Marc Lassonde

Keyword(s):

Lower Semicontinuous ◽

Mean Value ◽

Mean Value Property ◽

Lower Semicontinuous Functions ◽

Semicontinuous Functions

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Linear and nonlinear error bounds for lower semicontinuous functions

Optimization Letters ◽

10.1007/s11590-013-0648-z ◽

2013 ◽

Vol 8 (4) ◽

pp. 1301-1312 ◽

Cited By ~ 4

Author(s):

Mian-tao Chao ◽

Cao-zong Cheng

Keyword(s):

Error Bounds ◽

Lower Semicontinuous ◽

Nonlinear Error ◽

Lower Semicontinuous Functions ◽

Linear And Nonlinear ◽

Nonlinear Error Bounds ◽

Semicontinuous Functions

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On the Differences of Lower Semicontinuous Functions

Real Analysis Exchange ◽

10.14321/realanalexch.41.1.0123 ◽

2016 ◽

Vol 41 (1) ◽

pp. 123

Author(s):

Robert Menkyna

Keyword(s):

Lower Semicontinuous ◽

Lower Semicontinuous Functions ◽

Semicontinuous Functions

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Enlarged Inclusion of Subdifferentials

Canadian Mathematical Bulletin ◽

10.4153/cmb-2005-027-0 ◽

2005 ◽

Vol 48 (2) ◽

pp. 283-301 ◽

Cited By ~ 15

Author(s):

Lionel Thibault ◽

Dariusz Zagrodny

Keyword(s):

Lower Semicontinuous ◽

Lower Semicontinuous Functions ◽

The Difference ◽

Effective Domain ◽

Semicontinuous Functions

AbstractThis paper studies the integration of inclusion of subdifferentials. Under various verifiable conditions, we obtain that if two proper lower semicontinuous functions f and g have the subdifferential of f included in the γ-enlargement of the subdifferential of g, then the difference of those functions is γ-Lipschitz over their effective domain.

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