scholarly journals Relaxation and Purification for Nonconvex Variational Problems in Dual Banach Spaces: The Minimization Principle in Saturated Measure Spaces

2017 ◽  
Vol 55 (5) ◽  
pp. 3154-3170 ◽  
Author(s):  
Nobusumi Sagara
Keyword(s):  
Banach Spaces ◽  
Variational Problems ◽  
Minimization Principle ◽  
Measure Spaces ◽  
Nonconvex Variational Problems

Friedrichs extensions for nonconvex variational problems

1990 ◽  
Vol 14 (11) ◽  
pp. 905-914 ◽  
Author(s):  
Ioan R. Ionescu ◽  
Ioan Rosca
Keyword(s):  
Variational Problems ◽  
Nonconvex Variational Problems

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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