Existence and porosity for a class of perturbed optimization problems in Banach spaces

DOI10.1016/j.jmaa.2006.02.055zbMath1179.49001OpenAlexW1969308849MaRDI QIDQ853975

Li Hui Peng, Chong Li

Publication date: 7 December 2006

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2006.02.055

zbMATH Keywords

upper semicontinuous functionperturbed optimization problem\(\sigma\)-porous set\(G_{\delta }\)-subset

Mathematics Subject Classification ID

Sensitivity, stability, parametric optimization (90C31) Existence theories for problems in abstract spaces (49J27)

Related Items

Limiting subdifferentials of perturbed distance functions in Banach spaces ⋮ Well-posedness of a class of perturbed optimization problems in Banach spaces ⋮ Subdifferentials of perturbed distance function in Riemannian manifolds ⋮ Nearest and farthest points in spaces of curvature bounded below ⋮ Subdifferentials of a perturbed minimal time function in normed spaces

Cites Work

• Well-posed optimization problems
• Porosity of perturbed optimization problems in Banach spaces
• Factoring weakly compact operators
• Geometry of Banach spaces. Selected topics
• Farthest points in weakly compact sets
• Porosity of mutually nearest and mutually furthest points in Banach spaces.
• On well posedness of best simultaneous approximation problems in Banach spaces.
• Generic solutions for some perturbed optimization problem in non-reflexive Banach spaces
• Existence theorems for usual and approximate solutions of optimal control problems
• On well-posed mutually nearest and mutually furthest point problems in Banach spaces
• Generic existence of solutions for some perturbed optimization problems
• Existence de solutions pour des problèmes d'optimisation non convexe
• On generic well-posedness of restricted Chebyshev center problems in Banach spaces
• Farthest points in reflexive locally uniformly rotund Banach spaces
• Farthest points of sets in uniformly convex Banach spaces
• Fréchet differentiability of convex functions
• Porous Sets in Best Approximation Theory
• Nonconvex Optimization Problems Depending on a Parameter
• An Introduction to Banach Space Theory
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