A Unified Separation Theorem for Closed Sets in a Banach Space and Optimality Conditions for Vector Optimization

DOI10.1137/100811155zbMath1229.49018OpenAlexW2036254190MaRDI QIDQ3105779

Xi Yin Zheng, Ng Kung-fu

Publication date: 9 January 2012

Published in: SIAM Journal on Optimization (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/100811155

zbMATH Keywords

vector optimizationnormal coneseparation theoremapproximate Pareto solution

Mathematics Subject Classification ID

Convex programming (90C25) Multi-objective and goal programming (90C29) Nonsmooth analysis (49J52) Optimality conditions for free problems in two or more independent variables (49K10)

Related Items (11)

Necessary conditions for non-intersection of collections of sets ⋮ About extensions of the extremal principle ⋮ Connectedness of solution sets for generalized vector equilibrium problems via free-disposal sets in complete metric space ⋮ Vector optimization problems with generalized functional constraints in variable ordering structure setting ⋮ Connectedness of solution sets of strong vector equilibrium problems with an application ⋮ Lagrange multiplier rules for weak approximate Pareto solutions to constrained vector optimization problems with variable ordering structures ⋮ Strong Fermat rules for constrained set-valued optimization problems on Banach spaces ⋮ Exact separation theorem for disjoint closed sets in Hilbert spaces ⋮ Lagrange multiplier rules for weak approximate Pareto solutions of constrained vector optimization problems in Hilbert spaces ⋮ Hölder Continuity for Solution Mappings of Parametric Non-convex Strong Generalized Ky Fan Inequalities ⋮ Extremality, stationarity and generalized separation of collections of sets

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