Constrained convex optimization problems-well-posedness and stability*

DOI10.1080/01630569408816598zbMath0830.90119OpenAlexW2022799461MaRDI QIDQ4323507

A. S. Konsulova, Julian Petrov Revalski

Publication date: 22 February 1995

Published in: Numerical Functional Analysis and Optimization (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/01630569408816598

zbMATH Keywords

stabilityconstrained convex optimizationinequality in a partially ordered Banach space

Mathematics Subject Classification ID

Convex programming (90C25) Methods involving semicontinuity and convergence; relaxation (49J45)

Related Items (34)

Levitin-Polyak well-posedness for parametric quasivariational inequality problem of the Minty type ⋮ Levitin-Polyak well-posedness of variational inequality problems with functional constraints ⋮ The Levitin-Polyak well-posedness by perturbations for systems of general variational inclusion and disclusion problems ⋮ Generalized Levitin-Polyak well-posedness of vector equilibrium problems ⋮ The generalized Tykhonov well-posedness for system of vector quasi-equilibrium problems ⋮ Well-posedness of generalized vector quasivariational inequality problems ⋮ Levitin-Polyak well-posedness by perturbations for systems of set-valued vector quasi-equilibrium problems ⋮ Levitin-Polyak well-posedness for optimization problems with generalized equilibrium constraints ⋮ Characterizations of the nonemptiness and compactness for solution sets of convex set-valued optimization problems ⋮ Levitin-Polyak well-posedness of generalized vector quasi-equilibrium problems with functional constraints ⋮ Scalarization of Levitin–Polyak well-posed set optimization problems ⋮ Levitin-Polyak well-posedness in vector quasivariational inequality problems with functional constraints ⋮ Further study on the Levitin-Polyak well-posedness of constrained convex vector optimization problems ⋮ Levitin-Polyak Well-Posedness of Constrained Inverse Quasivariational Inequality ⋮ Well-posedness for convex symmetric vector quasi-equilibrium problems ⋮ Existence and well-posedness for symmetric vector quasi-equilibrium problems ⋮ LP well-posedness for bilevel vector equilibrium and optimization problems with equilibrium constraints ⋮ Levitin-Polyak well-posedness in generalized vector variational inequality problem with functional constraints ⋮ Levitin-Polyak well-posedness for lexicographic vector equilibrium problems ⋮ Levitin-Polyak well-posedness for equilibrium problems with functional constraints ⋮ The well-posedness for a system of generalized quasi-variational inclusion problems ⋮ Levitin-Polyak well-posedness for constrained quasiconvex vector optimization problems ⋮ \(\alpha\)-well-posedness for mixed quasi variational-like inequality problems ⋮ Levitin–Polyak Well-Posedness of Vector Variational Inequality Problems with Functional Constraints ⋮ Scalarization of Levitin-Polyak well-posedness in vector optimization using weak efficiency ⋮ Levitin-Polyak well-posedness of constrained vector optimization problems ⋮ Levitin-Polyak well-posedness for generalized semi-infinite multiobjective programming problems ⋮ Levitin-Polyak well-posedness of a system of generalized vector variational inequality problems ⋮ Levitin-Polyak well-posedness of generalized quasivariational inequalities with functional constraints ⋮ Levitin–Polyak well-posedness of symmetric vector quasi-equilibrium problems ⋮ Levitin-polyak well-posedness of vector equilibrium problems ⋮ Unnamed Item ⋮ Tykhonov well-posedness for lexicographic equilibrium problems ⋮ Generalized Levitin-Polyak Well-Posedness for Generalized Semi-Infinite Programs

Cites Work

• Unnamed Item
• Well-posed optimization problems
• Convergence of continuous linear functionals and their level sets
• Hadamard and Tyhonov well-posedness of a certain class of convex functions
• The topology of the \(\rho\)-Hausdorff distance
• Metrically well-set minimization problems
• Well-posed constrained optimization problems in metric spaces
• About well-posed optimization problems for functionals in metric spaces
• Convergence of convex sets and of solutions of variational inequalities
• Quantitative Stability of Variational Systems: I. The Epigraphical Distance
• The EPI-Distance Topology: Continuity and Stability Results with Applications to Convex Optimization Problems
• Weak Topologies for the Closed Subsets of a Metrizable Space
• Convex Optimization and the Epi-Distance Topology
• Operations on convergent families of sets and functions

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