New regularity conditions and Fenchel dualities for DC optimization problems involving composite functions

Optimization ◽  
2020 ◽  
pp. 1-27
Author(s):  
Donghui Fang ◽  
Qamrul Hasan Ansari ◽  
Jen-Chih Yao
Keyword(s):  
Optimization Problems ◽  
Regularity Conditions ◽  
Composite Functions ◽  
Dc Optimization

Regularity conditions and Farkas-type results for systems with fractional functions

2020 ◽  
Vol 54 (5) ◽  
pp. 1369-1384
Author(s):  
Xiangkai Sun ◽  
Xian-Jun Long ◽  
Liping Tang
Keyword(s):  
Optimization Problems ◽  
Regularity Conditions ◽  
Conjugate Duality ◽  
Conjugate Functions ◽  
Geometrical Constraint ◽  
Convex Constraint ◽  
Dc Optimization ◽  
Special Cases ◽  
Fractional Function

This paper deals with some new versions of Farkas-type results for a system involving cone convex constraint, a geometrical constraint as well as a fractional function. We first introduce some new notions of regularity conditions in terms of the epigraphs of the conjugate functions. By using these regularity conditions, we obtain some new Farkas-type results for this system using an approach based on the theory of conjugate duality for convex or DC optimization problems. Moreover, we also show that some recently obtained results in the literature can be rediscovered as special cases of our main results.

Hahn-Banach-Type Theorems and Subdifferentials for Invariant and Equivariant Order Continuous Vector Lattice-Valued Operators with Applications to Optimization

2021 ◽  
Vol 78 (1) ◽  
pp. 139-156
Author(s):  
Antonio Boccuto
Keyword(s):  
Optimality Conditions ◽  
Vector Lattice ◽  
Optimization Problems ◽  
Linear Constraints ◽  
Continuous Vector ◽  
Fixed Group ◽  
Composite Functions ◽  
Order Continuous

Abstract We give some versions of Hahn-Banach, sandwich, duality, Moreau--Rockafellar-type theorems, optimality conditions and a formula for the subdifferential of composite functions for order continuous vector lattice-valued operators, invariant or equivariant with respect to a fixed group G of homomorphisms. As applications to optimization problems with both convex and linear constraints, we present some Farkas and Kuhn-Tucker-type results.

Some characterizations of duality for DC optimization with composite functions

Optimization ◽  
2017 ◽  
Vol 66 (9) ◽  
pp. 1425-1443 ◽  
Author(s):  
Xiangkai Sun ◽  
Xian-Jun Long ◽  
Minghua Li
Keyword(s):  
Composite Functions ◽  
Dc Optimization

Convergence of Subdifferentials of Convexly Composite Functions

1999 ◽  
Vol 51 (2) ◽  
pp. 250-265 ◽  
Author(s):  
C. Combari ◽  
R. Poliquin ◽  
L. Thibault
Keyword(s):  
Banach Space ◽  
Constrained Optimization ◽  
Optimization Problems ◽  
Second Order ◽  
Constrained Optimization Problems ◽  
Composite Functions ◽  
Kuratowski Convergence ◽  
General Banach Space

AbstractIn this paper we establish conditions that guarantee, in the setting of a general Banach space, the Painlevé-Kuratowski convergence of the graphs of the subdifferentials of convexly composite functions. We also provide applications to the convergence of multipliers of families of constrained optimization problems and to the generalized second-order derivability of convexly composite functions.

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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