Limiting normal operator in quasiconvex analysis

DOI10.1007/s11228-015-0349-0zbMath1330.49011OpenAlexW2249814386MaRDI QIDQ904310

Miroslav Pištěk, Didier Aussel

Publication date: 13 January 2016

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

Full work available at URL: https://doi.org/10.1007/s11228-015-0349-0

zbMATH Keywords

constrained optimizationquasiconvex functionssemicontinuityquasimonotonicitysublevel setslimiting normal operator

Mathematics Subject Classification ID

Nonconvex programming, global optimization (90C26) Variational inequalities (49J40) Nonsmooth analysis (49J52) Set-valued and variational analysis (49J53) Convexity of real functions in one variable, generalizations (26A51) Convexity of real functions of several variables, generalizations (26B25) Optimality conditions for problems involving ordinary differential equations (49K15)

Related Items (7)

Stochastic quasi-subgradient method for stochastic quasi-convex feasibility problems ⋮ Interior quasi-subgradient method with non-Euclidean distances for constrained quasi-convex optimization problems in Hilbert spaces ⋮ Transformation of quasiconvex functions to eliminate local minima ⋮ Multiple-sets split quasi-convex feasibility problems: Adaptive subgradient methods with convergence guarantee ⋮ A continuity result for the adjusted normal cone operator ⋮ Existence results for quasi-variational inequalities with applications to Radner equilibrium problems. Resolution through variational inequalities ⋮ Quasi-convex feasibility problems: subgradient methods and convergence rates

Cites Work

• Quasimonotone quasivariational inequalities: existence results and applications
• Optimality conditions under relaxed quasiconvexity assumptions using star and adjusted subdifferentials
• Continuity properties of the normal cone to the level sets of a quasiconvex function
• An Appropriate Subdifferential for Quasiconvex Functions
• Fixed Point Theory, Variational Analysis, and Optimization
• Sequential formulae for the normal cone to sublevel sets
• Quasiconvex programming with locally starshaped constraint region and applications to quasiconvex MPEC
• Variational Analysis
• Adjusted Sublevel Sets, Normal Operator, and Quasi-convex Programming
• Set-valued analysis

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