Abstract convex approximations of nonsmooth functions

DOI10.1080/02331934.2013.869811zbMath1337.49021arXiv1810.00979OpenAlexW2013604529MaRDI QIDQ2808299

Maksim V. Dolgopolik

Publication date: 23 May 2016

Published in: Optimization (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1810.00979

zbMATH Keywords

nonsmooth analysisabstract codifferentiabilityabstract convex approximationabstract quasidifferentiability

Mathematics Subject Classification ID

Nonlinear programming (90C30) Nonsmooth analysis (49J52) Programming in abstract spaces (90C48) Optimality conditions for problems in abstract spaces (49K27)

Related Items (10)

Duality for composite optimization problem within the framework of abstract convexity ⋮ Zero duality gap conditions via abstract convexity ⋮ Metric regularity of quasidifferentiable mappings and optimality conditions for nonsmooth mathematical programming problems ⋮ Codifferentials and Quasidifferentials of the Expectation of Nonsmooth Random Integrands and Two-Stage Stochastic Programming ⋮ A convergence analysis of the method of codifferential descent ⋮ An extension of the Rådström cancellation theorem to cornets ⋮ New global optimality conditions for nonsmooth DC optimization problems ⋮ Constrained nonsmooth problems of the calculus of variations ⋮ A New Constraint Qualification and Sharp Optimality Conditions for Nonsmooth Mathematical Programming Problems in Terms of Quasidifferentials ⋮ The method of codifferential descent for convex and global piecewise affine optimization

Cites Work

• Unnamed Item
• Codifferential calculus in normed spaces
• Codifferential method for minimizing nonsmooth DC functions
• Nonsmooth analysis
• Semidifferentiable functions and necessary optimality conditions
• A method of truncated codifferential with application to some problems of cluster analysis
• Inhomogeneous convex approximations of nonsmooth functions
• Proper and adjoint exhausters in nonsmooth analysis: optimality conditions
• Calculus Without Derivatives
• A characterization of continuously codifferentiable functions and some consequences
• On locally-Lipschitz quasi-differentiate functions in Banach-spaces
• Optimality Conditions for Quasi-Differentiable Programs with Application to Two-Level Optimization
• Variational Analysis
• Fréchet quasidifferential calculus with applications to metric regularity of continuous maps
• An Embedding Theorem for Spaces of Convex Sets
• Applications of functional analysis and operator theory

This page was built for publication: Abstract convex approximations of nonsmooth functions