Variants of the Ekeland variational principle for a set-valued map involving the Clarke normal cone

DOI10.1016/j.jmaa.2005.04.044zbMath1089.49031OpenAlexW2045446464MaRDI QIDQ819712

Trúóng Xuân Dúc Hā

Publication date: 29 March 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.2005.04.044

zbMATH Keywords

vector optimizationEkeland variational principlecoderivativeClarke normal coneset-valued map

Mathematics Subject Classification ID

Multi-objective and goal programming (90C29) Nonsmooth analysis (49J52) Set-valued and variational analysis (49J53) Optimality conditions for problems in abstract spaces (49K27)

Related Items (9)

The Ekeland variational principle for Henig proper minimizers and super minimizers ⋮ Clarke coderivatives of efficient point multifunctions in parametric vector optimization ⋮ On Ekeland's variational principle for interval-valued functions with applications ⋮ On generalized Ekeland's variational principle and equivalent formulations for set-valued mappings ⋮ Existence of efficient and properly efficient solutions to problems of constrained vector optimization ⋮ A mountain pass-type theorem for vector-valued functions ⋮ On the existence of Pareto solutions for polynomial vector optimization problems ⋮ Optimality conditions for approximate Pareto solutions of a nonsmooth vector optimization problem with an infinite number of constraints ⋮ Existence of Pareto solutions for vector polynomial optimization problems with constraints

Cites Work

• Generalized differential calculus for nonsmooth and set-valued mappings
• The Ekeland variational principle for set-valued maps involving coderivatives
• General Ekeland's variational principle for set-valued mappings.
• On the variational principle
• Optimization and nonsmooth analysis
• Degrees of Efficiency and Degrees of Minimality
• Mean Value Property and Subdifferential Criteria for Lower Semicontinuous Functions
• New stability results for Ekeland's \(\varepsilon\) variational principles for vector-valued and set-valued maps
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