Directional Derivative Calculus and Optimality Conditions in Nonsmooth Mathematical Programming

DOI10.1080/02522667.1989.10698953zbMath0682.49016OpenAlexW2316420007MaRDI QIDQ4731726

Doug Ward

Publication date: 1989

Published in: Journal of Information and Optimization Sciences (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/02522667.1989.10698953

zbMATH Keywords

necessary optimality conditionschain rulesubgradientsgeneralized directional derivatives

Mathematics Subject Classification ID

Nonsmooth analysis (49J52) Programming in abstract spaces (90C48) Derivatives of functions in infinite-dimensional spaces (46G05) Optimality conditions for problems in abstract spaces (49K27)

Related Items (9)

Optimization on matrix manifold based on gradient information and its applications in network control ⋮ Separation of sets, Lagrange multipliers, and totally regular extremum problems ⋮ Upper DSL approximates and nonsmooth optimization ⋮ General constraint qualifications in nondifferentiable programming ⋮ Chain rules for nonsmooth functions ⋮ Nonsmooth invex functions and sufficient optimality conditions ⋮ Proximal point algorithm for differentiable quasi-convex multiobjective optimization ⋮ Differential stability in non-Lipschitzian optimization ⋮ Calculus for parabolic second-order derivatives

Cites Work

• Local convex analysis
• General constraint qualifications in nondifferentiable programming
• Weak Pareto-optimal necessary conditions in a nondifferentiable multiobjective program on a Banach space
• Duality in generalized linear fractional programming
• Optimization and nonsmooth analysis
• Extensions of subgradient calculus with applications to optimization
• On optimality conditions in nonsmooth inequality constrained minimization
• Nonsmooth Calculus in Finite Dimensions
• Isotone tangent cones and nonsmooth optimization
• The Quantificational Tangent Cones
• Shrinking generalized gradients
• Tangent Sets’ Calculus and Necessary Conditions for Extremality
• Tangent Cones, Generalized Gradients and Mathematical Programming in Banach Spaces
• Directionally Lipschitzian Functions and Subdifferential Calculus
• Convex Analysis

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