Results 141 to 150 of about 4,423 (156)

On pseudoconvex functions in Riemanian manifolds

2021
Let \(M\) be a Riemannian manifold and \(C \subset M\) a nonempty convex subset. A differentiable function \(f \colon C \to \mathbb{R}\) is called pseudoconvex if for each \(x,y \in C\) the relation \(\langle\mathrm{grad}\,f(x), \exp^{-1}_x y \rangle_x \geq 0\) implies \(f(y) \geq f(x).\) Some characterizations of pseudoconvex functions are presented.
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Second-Order Characterizations of Convex and Pseudoconvex Functions

Journal of Applied Analysis, 2003
Summary: The present paper gives characterizations of radially u.s.c. convex and pseudoconvex functions \(f: X\to\mathbb{R}\) defined on a convex subset \(X\) of a real linear space \(\mathbb{E}\) in terms of first- and second-order upper Dini-directional derivatives. Observing that the property \(f\) radially u.s.c.
IVANOV, IVAN GINCHEV, VSEVOLOD I. IVANOV
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H p -Functions on Strictly Pseudoconvex Domains

American Journal of Mathematics, 1976
Introduction. In this paper we study some questions concerning HP-functions on strictly pseudoconvex domains in CN. For the most part, the results we obtain are analogues of well known theorems in one variable. The first section is devoted to a few preliminaries about the Hardy classes on domains in CN.
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Minimizing pseudoconvex functions on convex compact sets

Journal of Optimization Theory and Applications, 1990
An algorithm is presented which minimizes continuously differentiable pseudo-convex functions on convex compact sets which are characterized by their support functions. If the function can be minimized exactly on affine sets in a finite number of operations and the constraints set is a polytope, the algorithm has finite convergence.
Higgins, J. E., Polak, E.
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Optimization and Variational Inequalities with Pseudoconvex Functions

Journal of Optimization Theory and Applications, 2010
The author defines a class of pseudoconvex functions in an extended sense and a notion of stationarity in an extended sense, which is called stationarity of order infinity. The inf-stationary points of infinite order are called extended inf-stationary points. Then it is proved that each global minimizer of a function \(f\) over a convex set \(X\) is an
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Relaxation methods of minimization of pseudoconvex functions

Journal of Soviet Mathematics, 1989
See the preview in Zbl 0501.65025.
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Some properties of nondifferentiable pseudoconvex functions

Mathematical Programming, 1983
It is shown that certain theorems concerning differentiable pseudoconvex functions can be extended to a class of nonsmooth pseudo-convex functions defined via the upper directional Dini derivative f'\({}_+(x;d)\) (instead of the usual linear mapping \()\).
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Subdifferential Properties of Quasiconvex and Pseudoconvex Functions: Unified Approach

Journal of Optimization Theory and Applications, 1998
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Strong comparison principle for q-pseudoconvex functions

2004
We announce some recent results, jointly obtained with E. Lanconelli, about a new class of curvature PDO's describing relevant properties of real hypersurfaces of C^{n+1}. In our setting the pseudoconvexity and the Levi form play the same role as the convexity and the real Hessian matrix play in the real Euclidean one.
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Holomorphic Lipschitz Functions in Pseudoconvex Domains

American Journal of Mathematics, 1979
Ahern, Patrick, Schneider, Robert
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