\(\varepsilon\)-optimality conditions for composed convex optimization problems

DOI10.1016/j.jat.2008.03.002zbMath1158.46029OpenAlexW2068717261MaRDI QIDQ935086

Gert Wanka, Radu Ioan Boţ, Ioan Bogdan Hodrea

Publication date: 31 July 2008

Published in: Journal of Approximation Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jat.2008.03.002

zbMATH Keywords

conjugate functions\(\varepsilon\)-optimality conditions\(\varepsilon\)-subdifferentialscomposed convex functions

Mathematics Subject Classification ID

Convex programming (90C25) Optimality conditions and duality in mathematical programming (90C46) Nonsmooth analysis (49J52) Applications of functional analysis in optimization, convex analysis, mathematical programming, economics (46N10) Duality theory (optimization) (49N15) Derivatives of functions in infinite-dimensional spaces (46G05)

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Cites Work

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• Some conjugation formulas and subdifferential formulas of convex analysis revisited
• Semi-continuous mappings in general topology
• A note on subdifferentials of convex composite functionals
• A weaker regularity condition for subdifferential calculus and Fenchel duality in infinite dimensional spaces.
• An alternative formulation for a new closed cone constraint qualification
• Necessary and sufficient conditions for stable conjugate duality
• Farkas-type results for inequality systems with composed convex functions via conjugate duality
• A new geometric condition for Fenchel's duality in infinite dimensional spaces
• Closedness conditions for the optimality of a family of non-convex optimization problems
• ε-Optimal solutions in nondifferentiable convex programming and some related questions

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