Asymptotic closure condition and Fenchel duality for DC optimization problems in locally convex spaces

2012 ◽  
Vol 75 (8) ◽  
pp. 3672-3681 ◽  
Author(s):  
D.H. Fang ◽  
C. Li ◽  
X.Q. Yang
Keyword(s):  
Optimization Problems ◽  
Fenchel Duality ◽  
Locally Convex Spaces ◽  
Closure Condition ◽  
Dc Optimization ◽  
Locally Convex ◽  
Convex Spaces

Characterizations of ɛ-duality gap statements for constrained optimization problems

2013 ◽  
Vol 11 (11) ◽  
Author(s):  
Horaţiu-Vasile Boncea ◽  
Sorin-Mihai Grad
Keyword(s):  
Constrained Optimization ◽  
Optimization Problems ◽  
Duality Gap ◽  
Regularity Conditions ◽  
Locally Convex Spaces ◽  
Zero Duality Gap ◽  
Constrained Optimization Problems ◽  
Locally Convex ◽  
Convex Spaces

AbstractIn this paper we present different regularity conditions that equivalently characterize various ɛ-duality gap statements (with ɛ ≥ 0) for constrained optimization problems and their Lagrange and Fenchel-Lagrange duals in separated locally convex spaces, respectively. These regularity conditions are formulated by using epigraphs and ɛ-subdifferentials. When ɛ = 0 we rediscover recent results on stable strong and total duality and zero duality gap from the literature.

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