On the notion of tangent cone in mathematical programming

DOI10.1080/02331939208843804zbMath0817.90108OpenAlexW2228685688MaRDI QIDQ4327928

Giorgio Giorgi, Angelo Guerraggio

Publication date: 27 March 1995

Published in: Optimization (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/02331939208843804

zbMATH Keywords

nonsmooth optimizationClarke's tangent conecontingent coneattainable conelocal cone approximations

Mathematics Subject Classification ID

Nonlinear programming (90C30) Nonsmooth analysis (49J52) Numerical methods based on nonlinear programming (49M37)

Related Items

Higher-order efficiency conditions for constrained vector equilibrium problems, On the notion of proper efficiency in vector optimization, Characterization of the cone of attainable directions, Strict lower semicontinuity of the level sets and invexity of a locally Lipschitz function, The supporting role of the Mangasarian-Fromovitz constraint qualification in calculus of variations, Dini and Hadamard directional derivatives in multiobjective optimization: an overview of some results, On the hierarchical structure of Pareto critical sets, Higher-order necessary and sufficient conditions for strict local pareto minima in terms of Studniarski's derivatives, Proper efficiency and proper Karush-Kuhn-Tucker conditions for smooth multiobjective optimization problems, Studniarski's derivatives and efficiency conditions for constrained vector equilibrium problems with applications, A relaxed constant positive linear dependence constraint qualification and applications, Strict efficiency in vector optimization, Second-order efficiency conditions for $C^{1,1}$-vector equilibrium problems in terms of contingent derivatives and applications, On a characterization of Clarke's tangent cone

Cites Work

• Tangency and differentiation: Some applications of convergence theory
• Sulla differenziabilita totale delle funzioni di piu variabili reali
• A course on optimization and best approximation
• On the cones of tangents with applications to mathematical programming
• Strong and Weak Convexity of Sets and Functions
• Cores of Tangent Cones and Clarke's Tangent Cone
• The Quantificational Tangent Cones
• Shrinking generalized gradients
• Approximation operators in optimization theory
• Tangent Sets’ Calculus and Necessary Conditions for Extremality
• Tangent Cones, Generalized Gradients and Mathematical Programming in Banach Spaces
• Regularity properties of open tangent cones
• A survey of conical approximations used in the optimization
• Constraint qualifications in maximization problems
• Extremum problems in the presence of restrictions
• Nonlinear Programming in Banach Space
• Generalized Kuhn–Tucker Conditions for Mathematical Programming Problems in a Banach Space
• A Necessary and Sufficient Qualification for Constrained Optimization
• Constraint Qualifications Revisited
• Set-valued analysis
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item