scholarly journals Linear regularity and ϕ-regularity of nonconvex sets

2007 ◽  
Vol 328 (1) ◽  
pp. 257-280 ◽  
Author(s):  
Kung Fu Ng ◽  
Rui Zang
Keyword(s):  
Nonconvex Sets ◽  
Linear Regularity

scholarly journals Cutting-Planes for Optimization of Convex Functions over Nonconvex Sets

2014 ◽  
Vol 24 (2) ◽  
pp. 643-677 ◽  
Author(s):  
Daniel Bienstock ◽  
Alexander Michalka
Keyword(s):  
Convex Functions ◽  
Cutting Planes ◽  
Nonconvex Sets

Uniform subsmoothness and linear regularity for a collection of infinitely many closed sets

2010 ◽  
Vol 73 (2) ◽  
pp. 413-430 ◽  
Author(s):  
Xiyin Zheng ◽  
Zhou Wei ◽  
Jen-Chih Yao
Keyword(s):  
Closed Sets ◽  
Linear Regularity

scholarly journals Linear Regularity for a Collection of Subsmooth Sets in Banach Spaces

2008 ◽  
Vol 19 (1) ◽  
pp. 62-76 ◽  
Author(s):  
Xi Yin Zheng ◽  
Kung Fu Ng
Keyword(s):  
Banach Spaces ◽  
Linear Regularity

scholarly journals Generalized Projections on Closed Nonconvex Sets in Uniformly Convex and Uniformly Smooth Banach Spaces

2015 ◽  
Vol 2015 ◽  
pp. 1-7 ◽  
Author(s):  
Messaoud Bounkhel
Keyword(s):  
Banach Space ◽  
Banach Spaces ◽  
Convex Set ◽  
Variational Problems ◽  
Generalized Projection ◽  
Uniformly Convex ◽  
Uniformly Smooth ◽  
Nonconvex Sets ◽  
Generalized Projections ◽  
Uniformly Smooth Banach Spaces

The present paper is devoted to the study of the generalized projectionπK:X∗→K, whereXis a uniformly convex and uniformly smooth Banach space andKis a nonempty closed (not necessarily convex) set inX. Our main result is the density of the pointsx∗∈X∗having unique generalized projection over nonempty close sets inX. Some minimisation principles are also established. An application to variational problems with nonconvex sets is presented.

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