Second-order optimality conditions with the envelope-like effect for nonsmooth vector optimization in infinite dimensions

DOI10.1016/J.NA.2012.09.013zbMath1280.90106OpenAlexW2085654956MaRDI QIDQ690947

Phan Quoc Khanh, Nguyen Dinh Tuan

Publication date: 29 November 2012

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.na.2012.09.013

zbMATH Keywords

weak solutionssecond-order optimality conditionsnonsmooth vector optimizationfirst and second-order approximations(strict) differentiabilityasymptotic \(p\)-compactnessenvelope-like effectfirm solutions

Mathematics Subject Classification ID

Multi-objective and goal programming (90C29) Optimality conditions and duality in mathematical programming (90C46) Nonsmooth analysis (49J52) Programming in abstract spaces (90C48)

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An Induction Theorem and Nonlinear Regularity Models ⋮ Second-order optimality conditions with the envelope-like effect for set-valued optimization ⋮ First and second-order optimality conditions without differentiability in multivalued vector optimization ⋮ First and second-order optimality conditions for nonsmooth vector optimization using set-valued directional derivatives ⋮ Second-order optimality conditions with the envelope-like effect in nonsmooth multiobjective mathematical programming. I: \(l\)-stability and set-valued directional derivatives ⋮ On necessary optimality conditions for nonsmooth vector optimization problems with mixed constraints in infinite dimensions ⋮ Second-order conditions for open-cone minimizers and firm minimizers in set-valued optimization subject to mixed constraints

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