Generalized Moreau–Rockafellar results for composed convex functions
From MaRDI portal
Publication:3646097
DOI10.1080/02331930902945082zbMath1201.90154OpenAlexW1984605028MaRDI QIDQ3646097
Gert Wanka, Radu Ioan Boţ, Sorin-Mihai Grad
Publication date: 19 November 2009
Published in: Optimization (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1080/02331930902945082
regularity conditionsconjugate functionsstable strong dualitycomposed convex functionsMoreau-Rockafellar results
Convex programming (90C25) Numerical optimization and variational techniques (65K10) Duality theory (optimization) (49N15)
Related Items
The stable duality of DC programs for composite convex functions ⋮ Stable and total Fenchel duality for composed convex optimization problems ⋮ Optimality conditions of quasi $(\alpha,\varepsilon)$-solutions and approximate mixed type duality for DC composite optimization problems ⋮ Some characterizations of duality for DC optimization with composite functions ⋮ Approximate optimality conditions for composite convex optimization problems ⋮ Infimal convolution, \( c \)-subdifferentiability, and Fenchel duality in evenly convex optimization ⋮ Optimization of first-order Nicoletti boundary value problem with discrete and differential inclusions and duality ⋮ Optimality conditions for composite DC infinite programming problems ⋮ Extended Farkas lemma and strong duality for composite optimization problems with DC functions ⋮ Necessary and sufficient conditions for strong Fenchel-Lagrange duality via a coupling conjugation scheme ⋮ The Toland-Fenchel-Lagrange duality of DC programs for composite convex functions ⋮ Characterizations of \(\varepsilon\)-duality gap statements for constrained optimization problems ⋮ A note on optimality conditions for DC programs involving composite functions ⋮ Extended Farkas's lemmas and strong dualities for conic programming involving composite functions ⋮ Revisiting some rules of convex analysis ⋮ Characterizations of \(\varepsilon\)-duality gap statements for composed optimization problems ⋮ The stable Farkas lemma for composite convex functions in infinite dimensional spaces ⋮ On biconjugates of infimal functions ⋮ Optimality conditions and total dualities for conic programming involving composite function ⋮ Dual representations for systemic risk measures ⋮ New regularity conditions and Fenchel dualities for DC optimization problems involving composite functions ⋮ Optimality conditions of Fenchel-Lagrange duality and Farkas-type results for composite DC infinite programs ⋮ High-Order Optimization Methods for Fully Composite Problems ⋮ A Study of Convex Convex-Composite Functions via Infimal Convolution with Applications
Cites Work
- Semi-continuous mappings in general topology
- On strong and total Lagrange duality for convex optimization problems
- A weaker regularity condition for subdifferential calculus and Fenchel duality in infinite dimensional spaces.
- Necessary and sufficient conditions for stable conjugate duality
- A new constraint qualification for the formula of the subdifferential of composed convex functions in infinite dimensional spaces