Second-order necessary and sufficient conditions in nonsmooth optimization

DOI10.1007/BF01581156zbMath0824.90123MaRDI QIDQ1337142

V. Pereyra

Publication date: 30 October 1994

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

zbMATH Keywords

nonsmooth optimizationsecond derivativessecond-order necessary and sufficient optimality conditions

Mathematics Subject Classification ID

Nonlinear programming (90C30) Nonsmooth analysis (49J52) Programming in abstract spaces (90C48)

Related Items (18)

Calculus of directional subdifferentials and coderivatives in Banach spaces ⋮ On the relations between some second-order derivatives ⋮ An Interior-Point $$\boldsymbol{\ell_{1}}$$ -Penalty Method for Nonlinear Optimization ⋮ Second-order optimality conditions for inequality constrained problems with locally Lipschitz data ⋮ Calculus of directional coderivatives and normal cones in Asplund spaces ⋮ Higher-Order Optimality Conditions and Higher-Order Tangent Sets ⋮ Directionally limiting subdifferentials and second-order optimality conditions ⋮ Second-order optimality conditions with arbitrary nondifferentiable function in scalar and vector optimization ⋮ On second-order conditions in unconstrained optimization ⋮ Conciliating Generalized Derivatives ⋮ Separate necessary and sufficient conditions for the local minimum of a function ⋮ Parameter-free duality models and applications to semi-infinite minmax fractional programming based on second-order (\(\phi,\eta ,\rho ,\theta,\tilde{m}\))-sonvexities ⋮ Optimality conditions for an isolated minimum of order two in \(C1\) constrained optimization ⋮ Fréchet approach in second-order optimization ⋮ The check of optimality conditions in nonsmooth programming ⋮ Higher order optimality conditions with an arbitrary non-differentiable function ⋮ Second-order optimality conditions for minimizing a max-function ⋮ A derivative-free algorithm for constrained global optimization based on exact penalty functions

Cites Work

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• A Generalized Second-Order Derivative in Nonsmooth Optimization
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• Second-Order Optimality Conditions in Nonlinear Programming Obtained by Way of Epi-Derivatives
• Optimization and nonsmooth analysis
• Second-Order Necessary Conditions in Constrained Semismooth Optimization
• Second-Order Sufficient Conditions in Nonsmooth Optimization
• Necessary and sufficient optimality conditions for a class of nonsmooth minimization problems
• A unified theory of first and second order conditions for extremum problems in topological vector spaces
• Semismooth and Semiconvex Functions in Constrained Optimization
• A General Sufficiency Theorem for Nonsmooth Nonlinear Programming

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