A note on quasiconvex functions that are pseudoconvex.

Giorgio Giorgi

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Displaying similar documents to “A note on quasiconvex functions that are pseudoconvex.”

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.

Local completeness of locally pseudoconvex spaces and Borwein-Preiss variational principle

J. H. Qiu, S. Rolewicz (2007)

Studia Mathematica

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The notion of local completeness is extended to locally pseudoconvex spaces. Then a general version of the Borwein-Preiss variational principle in locally complete locally pseudoconvex spaces is given, where the perturbation is an infinite sum involving differentiable real-valued functions and subadditive functionals. From this, some particular versions of the Borwein-Preiss variational principle are derived. In particular, a version with respect to the Minkowski gauge of a bounded closed...

Some remarks about strictly pseudoconvex functions with respect to the Clarke-Rockafellar subdifferential.

Samir, Lahrech, Abdessamad, Jaddar, Abdelmalek, Ouahab, Abderrahim, Mbarki (2006)

Lobachevskii Journal of Mathematics

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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.

Pseudoconvex domains on complex spaces with singularities

Mihnea Coltoiu, Nicolae Mihalache (1989)

Compositio Mathematica

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Characterizations of the Solution Sets of Generalized Convex Minimization Problems

Ivanov, Vsevolod (2003)

Serdica Mathematical Journal

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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.

Locally m-pseudoconvex topologies on locally A-pseudoconvex algebras

M. Abel, J. Arhippainen (2004)

Czechoslovak Mathematical Journal

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Let $(A, T)$ be a locally A-pseudoconvex algebra over $ℝ$ or $ℂ$ . We define a new topology $m (T)$ on $A$ which is the weakest among all m-pseudoconvex topologies on $A$ stronger than $T$ . We describe a family of non-homogeneous seminorms on $A$ which defines the topology $m (T)$ .

The strongest vector space topology is locally convex on separable linear subspaces

W. Żelazko (1997)

Annales Polonici Mathematici

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Let X be a real or complex vector space equipped with the strongest vector space topology $τ_{m a x}$ . Besides the result announced in the title we prove that X is uncountable-dimensional if and only if it is not locally pseudoconvex.

A smooth Pseudoconvex domain without pseudoconvex exhaustion.

Klas Diederich, John Erik Fornaess (1982)

Manuscripta mathematica

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A non-locally convex topological algebra with all commutative subalgebras locally convex

W. Żelazko (1996)

Studia Mathematica

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We construct a complete multiplicatively pseudoconvex algebra with the property announced in the title. This solves Problem 25 of [6].

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.