Variational convexity and the local monotonicity of subgradient mappings

DOI10.1007/s10013-019-00339-5zbMath1428.49021OpenAlexW2922760259WikidataQ128177646 ScholiaQ128177646MaRDI QIDQ2330971

R. Tyrrell Rockafellar

Publication date: 23 October 2019

Published in: Vietnam Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10013-019-00339-5

zbMATH Keywords

local minimumlocal monotonicitytilt stabilitysubgradient mappingvariational convexityproximal point iterations

Mathematics Subject Classification ID

Sensitivity, stability, parametric optimization (90C31) Set-valued and variational analysis (49J53) Set-valued and function-space-valued mappings on manifolds (58C06)

Related Items

Convergence of augmented Lagrangian methods in extensions beyond nonlinear programming, Strong Variational Sufficiency for Nonlinear Semidefinite Programming and Its Implications, Augmented Lagrangians and hidden convexity in sufficient conditions for local optimality, Variational Convexity of Functions and Variational Sufficiency in Optimization, Generic linear convergence through metric subregularity in a variable-metric extension of the proximal point algorithm, A Chain Rule for Strict Twice Epi-Differentiability and Its Applications, Progressive decoupling of linkages in optimization and variational inequalities with elicitable convexity or monotonicity, On the positive definiteness of limiting coderivative for set-valued mappings, Quadratic Growth and Strong Metric Subregularity of the Subdifferential via Subgradient Graphical Derivative

Cites Work

• Second-order variational analysis and characterizations of tilt-stable optimal solutions in infinite-dimensional spaces
• On the Douglas-Rachford splitting method and the proximal point algorithm for maximal monotone operators
• Characterizations of Full Stability in Constrained Optimization
• Monotone Operators and the Proximal Point Algorithm
• Variational Analysis
• Tilt Stability of a Local Minimum
• Subgradient monotonicity and convex functions
• Prox-regular functions in variational analysis
• Stability of Locally Optimal Solutions
• Variational Analysis of Regular Mappings
• Second-order growth, tilt stability, and metric regularity of the subdifferential
• Full Stability in Finite-Dimensional Optimization
• Tilt Stability, Uniform Quadratic Growth, and Strong Metric Regularity of the Subdifferential
• Proximité et dualité dans un espace hilbertien
• Local Convergence of the Proximal Point Algorithm and Multiplier Methods Without Monotonicity