Second-Order Characterizations of Convex and Pseudoconvex Functions

DOI10.1515/JAA.2003.261zbMath1040.49024OpenAlexW2108681040MaRDI QIDQ4467305

Ivan Ginchev, Vsevolod I. Ivanov

Publication date: 9 June 2004

Published in: Journal of Applied Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1515/jaa.2003.261

zbMATH Keywords

nonsmooth analysisconvex functionupper semicontinuitypseudoconvex functionssecond-order Dini-directional derivativesusc

Mathematics Subject Classification ID

Convex programming (90C25) Nonconvex programming, global optimization (90C26) Nonsmooth analysis (49J52) Convexity of real functions of several variables, generalizations (26B25) Nondifferentiability (nondifferentiable functions, points of nondifferentiability), discontinuous derivatives (26A27)

Related Items (10)

Equilibrium uniqueness in aggregative games: very practical conditions ⋮ Second-order subdifferentials and convexity of real-valued functions ⋮ Characterizing convexity of a function by its Fréchet and limiting second-order subdifferentials ⋮ Characterizations of pseudoconvex functions and semistrictly quasiconvex ones ⋮ Aggregative variational inequalities ⋮ Second-order characterizations of quasiconvexity and pseudoconvexity for differentiable functions with Lipschitzian derivatives ⋮ Second-order optimality conditions for efficiency in \(C^{1,1}\)-smooth quasiconvex multiobjective programming problem ⋮ On Strict Pseudoconvexity ⋮ Characterization of radially lower semicontinuous pseudoconvex functions ⋮ Second-order characterization of convex functions and its applications

Cites Work

• Unnamed Item
• Second-order directional derivatives for nonsmooth functions
• Nine kinds of quasiconcavity and concavity
• Generalized second-order characterizations of convex functions
• Some properties of nondifferentiable pseudoconvex functions
• Criteria for quasi-convexity and pseudo-convexity: Relationships and comparisons
• Generalized second-order directional derivatives and optimization with C^1,1 functions
• On Lower Bounds of the Second-Order Directional Derivatives of Ben-Tal, Zowe, and Chaney

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