Convex Optimization and the Epi-Distance Topology

DOI10.2307/2001823zbMath0681.46013OpenAlexW4256302257MaRDI QIDQ4730285

Roberto Lucchetti, Gerald A. Beer

Publication date: 1991

Full work available at URL: https://doi.org/10.2307/2001823

zbMATH Keywords

convex optimizationMosco convergenceChebyshev setapproximative compactnessmetric projectionswell-posed minimization problemepi-distance topologylower semicontinuous convex functions

Mathematics Subject Classification ID

Nonsmooth analysis (49J52) Function spaces in general topology (54C35) Topological linear spaces of continuous, differentiable or analytic functions (46E10) Convergence in general topology (sequences, filters, limits, convergence spaces, nets, etc.) (54A20) Convex sets in topological linear spaces; Choquet theory (46A55) Derivatives of functions in infinite-dimensional spaces (46G05)

Related Items

Well-posed optimization problems and a new topology for the closed subsets of a metric space ⋮ Stability of the geometric Ekeland variational principle: Convex case ⋮ Lipschitz behaviour of the Legendre-Fenchel transform ⋮ Ambiguous loci of mutually nearest and mutually furthest points in Banach spaces ⋮ On the Fell topology ⋮ On well-posed mutually nearest and mutually furthest point problems in Banach spaces ⋮ Apart sets and functions: an application to the stability of penalized optimization problems ⋮ Polar locally convex topologies and Attouch-Wets convergence ⋮ Sequential characterization of statistical epi-convergence ⋮ Quantitative stability analysis for maximal monotone operators and semi-groups of contractions ⋮ Lipschitz Regularization and the Convergence of Convex Functions ⋮ Approximations and solution estimates in optimization ⋮ Recent hypertopologies and continuity of the value function and of the constrained level sets ⋮ A second look at set convergence and linear analysis ⋮ Minimizing irregular convex functions: Ulam stability for approximate minima ⋮ The slice topology: a viable alternative to mosco convergence in nonreflexive spaces ⋮ Constrained convex optimization problems-well-posedness and stability^* ⋮ Bornological convergence and shields ⋮ Convergence on closed convex sets in a locally convex space ⋮ Porosity of mutually nearest and mutually furthest points in Banach spaces. ⋮ Generic well posedness of supinf problems ⋮ On mutually nearest and mutually farthest points in reflexive Banach spaces ⋮ Stability results of a class of well-posed optimization problems ⋮ Persistence and stability of solutions of Hamilton-Jacobi equations ⋮ On mutually nearest and mutually furthest points of sets in Banach spaces ⋮ Efficiency and the uniform linear minorization of convex functions ⋮ Generic well-posedness of minimization problems with mixed continuous constraints. ⋮ Continuity of the Legendre–Fenchel transform for some variational convergences ⋮ Density of the set of local minimizers for a generic cost function ⋮ Generic well-posedness of minimization problems with mixed smooth constraints ⋮ Attouch-Wets Convergence and a Differential Operator for Convex Functions ⋮ The \(\varepsilon\)-strategy in variational analysis: illustration with the closed convexification of a function ⋮ Analyse de récession et résultats de stabilité d'une convergence variationnelle, application à la théorie de la dualité en programmation mathématique ⋮ On the convergence of subdifferentials of convex functions ⋮ A Characterization of Epi-Convergence in Terms of Convergence of Level Sets ⋮ Gap, excess and bornological convergence ⋮ Boundedly UC spaces and topologies on function spaces ⋮ Weak Topologies for the Closed Subsets of a Metrizable Space ⋮ Slice convergence: stabilité et optimisation dans les espaces non réflexifs ⋮ Strongly Convex Functions, Moreau Envelopes, and the Generic Nature of Convex Functions with Strong Minimizers ⋮ A necessary and sufficient condition on the stability of the infimum of convex functions ⋮ Stability and Error Analysis for Optimization and Generalized Equations ⋮ Convergence of epigraphs and of sublevel sets ⋮ Convergence of fuzzy sets with respect to the supremum metric ⋮ Uniform Continuity on Bounded Sets and the Attouch-Wets Topology ⋮ ON ALMOST WELL-POSED MUTUALLY NEAREST AND MUTUALLY FURTHEST POINT PROBLEMS

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Some new results on smoothness and rotundity in normed linear spaces
• Quasi-uniformization of hyperspaces and convergence of nets of semicontinuous multifunctions
• The strong Ekeland variational principle, the strong drop theorem and applications
• Convergence of continuous linear functionals and their level sets
• Continuity of the Fenchel correspondence and continuity of polarities
• The topology of the \(\rho\)-Hausdorff distance
• Convex analysis and measurable multifunctions
• Uniform convergence of probability measures: Topological criteria
• Three characterizations of the Mosco topology for convex functions
• Une famille de topologies sur l'ensemble des fonctions convexes pour lesquelles la polarite est bicontinue
• About well-posed optimization problems for functionals in metric spaces
• Convergence of convex sets and of solutions of variational inequalities
• A course on optimization and best approximation
• On the continuity of the Young-Fenchel transform
• On the Young-Fenchel Transform for Convex Functions
• On Mosco convergence of convex sets
• Mosco Convergence and the Kadec Property
• On the Convergence of Sequences of Convex Sets in Finite Dimensions
• Quantitative Stability of Variational Systems: I. The Epigraphical Distance
• Conjugate Convex Functions and the Epi-Distance Topology
• Minima of quasi-convex functions
• Convergence of Sequences of Convex Sets, Cones and Functions. II
• Gradients of Convex Functions
• Convex Analysis
• Operations on convergent families of sets and functions

This page was built for publication: Convex Optimization and the Epi-Distance Topology