Displaying similar documents to “Convexity, C-convexity and Pseudoconvexity Изпъкналост, c-изпъкналост и псевдоизпъкналост”

Characterizations of the Solution Sets of Generalized Convex Minimization Problems

Ivanov, Vsevolod (2003)

Serdica Mathematical Journal

Similarity:

2000 Mathematics Subject Classification: 90C26, 90C20, 49J52, 47H05, 47J20. In this paper we obtain some simple characterizations of the solution sets of a pseudoconvex program and a variational inequality. Similar characterizations of the solution set of a quasiconvex quadratic program are derived. Applications of these characterizations are given.

Lempert theorem for strongly linearly convex domains

Łukasz Kosiński, Tomasz Warszawski (2013)

Annales Polonici Mathematici

Similarity:

In 1984 L. Lempert showed that the Lempert function and the Carathéodory distance coincide on non-planar bounded strongly linearly convex domains with real-analytic boundaries. Following his paper, we present a slightly modified and more detailed version of the proof. Moreover, the Lempert Theorem is proved for non-planar bounded strongly linearly convex domains.

A note on strong pseudoconvexity

Vsevolod Ivanov (2008)

Open Mathematics

Similarity:

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

First Order Characterizations of Pseudoconvex Functions

Ivanov, Vsevolod (2001)

Serdica Mathematical Journal

Similarity:

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.