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On Strict Pseudoconvexity
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V. I. Ivanov
Published/Copyright:
June 9, 2010
Abstract
The present paper provides first and second-order characterizations of a radially lower semicontinuous strictly pseudoconvex function ƒ : X → ℝ defined on a convex set X in the real Euclidean space ℝn in terms of the lower Dini-directional derivative. In particular we obtain connections between the strictly pseudoconvex functions, nonlinear programming problem, Stampacchia variational inequality, and strict Minty variational inequality. We extend to the radially continuous functions the characterization due to Diewert, Avriel, Zang [J. Econom. Theory 25: 397–420, 1981]. A new implication appears in our conditions. Connections with other classes of functions are also derived.
Key words and phrases.: Generalized convexity; strict pseudoconvexity; nonsmooth analysis; nonsmooth optimization; Dini-directional derivatives
Received: 2005-03-29
Revised: 2006-06-07
Published Online: 2010-06-09
Published in Print: 2007-December
© Heldermann Verlag
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Keywords for this article
Generalized convexity;
strict pseudoconvexity;
nonsmooth analysis;
nonsmooth optimization;
Dini-directional derivatives
Articles in the same Issue
- Existence of Solutions for Unilateral Problems in L1 Involving Lower Order Terms in Divergence form in Orlicz Spaces
- On Strict Pseudoconvexity
- Differential Criterion of n-Dimensional Geometrically Convex Functions
- Continuity Properties of the Stress Tensor in the 3-Dimensional Ramberg/Osgood Model
- Weinstein's Technique for a Class of Parabolic Problems
- On the Uniqueness of Measure and Category σ-Ideals on 2ω
- -Best Approximation of a γ-Regular Function
- A Lévy-Ciesielski Expansion for Quantum Brownian Motion and the Construction of Quantum Brownian Bridges
- Generalized Vector Variational Inequalities in Topological Vector Spaces
- Erratum to the Paper “A Note on Stability of Solutions for Abstract Semilinear Dirichlet Problems”
