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Displaying similar documents to “Characterizations of the Solution Sets of Generalized Convex Minimization Problems”

First Order Characterizations of Pseudoconvex Functions

Ivanov, Vsevolod (2001)

Serdica Mathematical Journal

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First order characterizations of pseudoconvex functions are investigated in terms of generalized directional derivatives. A connection with the invexity is analysed. Well-known first order characterizations of the solution sets of pseudolinear programs are generalized to the case of pseudoconvex programs. The concepts of pseudoconvexity and invexity do not depend on a single definition of the generalized directional derivative.

A note on strong pseudoconvexity

Vsevolod Ivanov (2008)

Open Mathematics

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A strongly pseudoconvex function is generalized to non-smooth settings. A complete characterization of the strongly pseudoconvex radially lower semicontinuous functions is obtained.

Convexity, C-convexity and Pseudoconvexity Изпъкналост, c-изпъкналост и псевдоизпъкналост

Nikolov, Nikolai (2011)

Union of Bulgarian Mathematicians

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Николай М. Николов - Разгледани са характеризации на различни понятия за изпъкналост, като тези понятия са сравнени. We discuss different characterizations of various notions of convexity as well as we compare these notions. *2000 Mathematics Subject Classification: 32F17.

A note on quasiconvex functions that are pseudoconvex.

Giorgio Giorgi (1987)

Trabajos de Investigación Operativa

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In the present note we consider the definitions and properties of locally pseudo- and quasiconvex functions and give a sufficient condition for a locally quasiconvex function at a point x ∈ R, to be also locally pseudoconvex at the same point.

First-Order Conditions for Optimization Problems with Quasiconvex Inequality Constraints

Ginchev, Ivan, Ivanov, Vsevolod I. (2008)

Serdica Mathematical Journal

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2000 Mathematics Subject Classification: 90C46, 90C26, 26B25, 49J52. The constrained optimization problem min f(x), gj(x) ≤ 0 (j = 1,…p) is considered, where f : X → R and gj : X → R are nonsmooth functions with domain X ⊂ Rn. First-order necessary and first-order sufficient optimality conditions are obtained when gj are quasiconvex functions. Two are the main features of the paper: to treat nonsmooth problems it makes use of Dini derivatives; to obtain more sensitive conditions,...