The upper and lower second order directional derivatives of a sup-type function

DOI10.1007/BF01580771zbMath0900.49011MaRDI QIDQ1813158

Hidefumi Kawasaki

Publication date: 25 June 1992

Published in: Mathematical Programming. Series A. Series B (Search for Journal in Brave)

Mathematics Subject Classification ID

Nonlinear programming (90C30) Nonsmooth analysis (49J52) Differentiation theory (Gateaux, Fréchet, etc.) on manifolds (58C20)

Related Items (15)

Metric regularity and second-order necessary optimality conditions for minimization problems under inclusion constraints ⋮ On second-order directional derivatives ⋮ Lazy orbits: an optimization problem on the sphere ⋮ Variational analysis of a composite function: A formula for the lower second order epi-derivative ⋮ Second-order necessary and sufficient optimality conditions for minimizing a sup-type function ⋮ No-gap second-order optimality conditions for optimal control problems with a single state constraint and control ⋮ Unnamed Item ⋮ A chain rule for parabolic second-order epiderivatives ⋮ On parametric nonlinear programming ⋮ On necessary optimality conditions for nonsmooth vector optimization problems with mixed constraints in infinite dimensions ⋮ Semi-infinite programming, duality, discretization and optimality conditions† ⋮ Second-order optimality conditions for minimizing a max-function ⋮ Second order necessary optimality conditions for minimizing a sup-type function ⋮ On relations and applications of generalized second-order directional derivatives ⋮ Calculus for parabolic second-order derivatives

Cites Work

• Approximate first-order and second-order directional derivatives of a marginal function in convex optimization
• Technical note: Directional derivatives in nonsmooth optimization
• An envelope-like effect of infinitely many inequality constraints on second-order necessary conditions for minimization problems
• Second-order necessary and sufficient optimality conditions for minimizing a sup-type function
• Limiting behaviour of the approximate first order and second order directional derivatives for a convex function
• Second-Order Derivatives of Extremal-Value Functions and Optimality Conditions for Semi-Infinite Programs
• A unified theory of first and second order conditions for extremum problems in topological vector spaces
• Expansion with respect to a parameter of the extremal values of game problems
• On the differential properties of the support function of the∈-subdifferential of a convex function
• Approximating a Second-Order Directional Derivative for Nonsmooth Convex Functions

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