Convergence of epigraphs and of sublevel sets

DOI10.1007/BF01027690zbMath0797.49023MaRDI QIDQ1308948

Roberto Lucchetti, Gerald A. Beer

Publication date: 1 November 1995

Published in: Set-Valued Analysis (Search for Journal in Brave)

zbMATH Keywords

bounded proximal topologyhyperspace topologieswell-posed function

Mathematics Subject Classification ID

Sensitivity, stability, well-posedness (49K40) Hyperspaces in general topology (54B20) Function spaces in general topology (54C35)

Related Items

Convergence of the efficient sets ⋮ Well-set and well-posed minimization problems ⋮ Recent hypertopologies and continuity of the value function and of the constrained level sets ⋮ Graph Convergence of Set-Valued Maps and its Relationship to Other Convergences ⋮ On Choquet theorem for random upper semicontinuous functions ⋮ On the upper semicontinuity of Choquet capacities

Cites Work

• Tangency and differentiation: Some applications of convergence theory
• The topology of the \(\rho\)-Hausdorff distance
• Scalar convergence of convex sets
• A stability result in quasi-convex programming
• Well-posed optimization problems and a new topology for the closed subsets of a metric space
• Set convergences: A survey and a classification
• On the continuity of the Young-Fenchel transform
• Support and distance functionals for convex sets
• On some inverse stability problems for the epigraphical sum
• Quantitative Stability of Variational Systems: I. The Epigraphical Distance
• A Characterization of Epi-Convergence in Terms of Convergence of Level Sets
• Weak Topologies for the Closed Subsets of a Metrizable Space
• Wijsman convergence of convex sets under renorming
• Convex Optimization and the Epi-Distance Topology
• Minima of quasi-convex functions
• Convergence of Sequences of Convex Sets, Cones and Functions. II
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