Exhausters and subdifferentials in non-smooth analysis

DOI10.1080/02331930701778825zbMath1220.49007OpenAlexW2050930406MaRDI QIDQ5449010

Vera Roshchina, V. F. Dem'yanov

Publication date: 10 March 2008

Published in: Optimization (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/02331930701778825

zbMATH Keywords

Clarke subdifferentialFréchet subdifferentialMichel-Penot subdifferentialpositively homogeneous functionupper and lower exhaustersGâteaux subdifferential

Mathematics Subject Classification ID

Optimality conditions and duality in mathematical programming (90C46) Nonsmooth analysis (49J52) Set-valued and variational analysis (49J53) Convexity of real functions of several variables, generalizations (26B25)

Related Items (17)

Unnamed Item ⋮ Proper and adjoint exhausters in nonsmooth analysis: optimality conditions ⋮ Positively homogeneous functions revisited ⋮ Adjoint coexhausters in nonsmooth analysis and extremality conditions ⋮ Exhausters and implicit functions in nonsmooth systems ⋮ Exact calculus of Fréchet subdifferentials for Hadamard directionally differentiable functions ⋮ Reduction of finite exhausters ⋮ Alternance Form of Optimality Conditions in the Finite-Dimensional Space ⋮ Implicit function theorem for nonsmooth systems by means of exhausters ⋮ On minimal representations by a family of sublinear functions ⋮ On methods for converting exhausters of positively homogeneous functions ⋮ Minimal convex majorants of functions and Demyanov–Rubinov exhaustive super(sub)differentials ⋮ On reduction of exhausters via a support function representation ⋮ Optimal control problem for switched system with the nonsmooth cost functional ⋮ Some relationships among quasidifferential, weak subdifferential and exhausters ⋮ Reduction of weak exhausters and optimality conditions via reduced weak exhausters ⋮ Proper exhausters and coexhausters in nonsmooth analysis

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• On the cones of tangents with applications to mathematical programming
• Optimality conditions in terms of upper and lower exhausters
• Exhausters af a positively homogeneous function^*
• A survey of subdifferential calculus with applications
• Nonsmooth sequential analysis in Asplund spaces

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