Stable and Total Fenchel Duality for DC Optimization Problems in Locally Convex Spaces

2011 ◽  
Vol 21 (3) ◽  
pp. 730-760 ◽  
Author(s):  
D. H. Fang ◽  
C. Li ◽  
X. Q. Yang
Keyword(s):  
Optimization Problems ◽  
Fenchel Duality ◽  
Locally Convex Spaces ◽  
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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