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Convex Defining Functions for Convex Domains [PDF]
Journal of Geometric Analysis, 2010 21 ...
Jeffery D. McNeal, A. K. Herbig
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Convex Functions on Convex Polytopes [PDF]
Proceedings of the American Mathematical Society, 1968 The behavior of convex functions is of interest in connection with a wide variety of optimization problems. It is shown here that this behavior is especially simple, in certain respects, when the domain is a polytope or belongs to certain classes of sets closely related to polytopes; moreover, the polytopes and related classes are actually ...
David Gale +2 more
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Valuations on Convex Functions [PDF]
International Mathematics Research Notices, 2017 All continuous, SL$(n)$ and translation invariant valuations on the space of convex functions on ${\mathbb R}^n$ are completely classified.
Andrea Colesanti +2 more
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Radical Convex Functions [PDF]
Mediterranean Journal of Mathematics, 2021 to appear in Mediterr.
Mohammad Sababheh, Hamid Reza Moradi
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Smooth convex extensions of convex functions [PDF]
Calculus of Variations and Partial Differential Equations, 2019 Final ...
Azagra, Daniel, Mudarra, Carlos
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Schur-Convexity of Averages of Convex Functions [PDF]
Journal of Inequalities and Applications, 2011 The object is to give an overview of the study of Schur-convexity of various means and functions and to contribute to the subject with some new results. First, Schur-convexity of the generalized integral and weighted integral quasi-arithmetic mean is studied.
Roqia Ghulam +3 more
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On the singularities of convex functions [PDF]
Manuscripta Mathematica, 1992 Given a semi-convex functionu: ω⊂R n→R and an integerk≡[0,1,n], we show that the set ∑k defined by $$\Sigma ^k = \left\{ {x \in \Omega :dim\left( {\partial u\left( x \right)} \right) \geqslant k} \right\}$$ is countably ℋn-k i.e., it is ...
Alberti G, AMBROSIO, Luigi, Cannarsa P.
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On φ-convexity of convex functions
Linear Algebra and its Applications, 1998 AbstractWe construct a non-trivial set φ of extended-real valued functions on Rn, containing all affine functions, such that an extended-real valued function f on Rn is convex if and only if it is φ-convex in the sense of Dolecki and Kurcyusz, i.e., the (pointwise) supremum of some subset of φ. Also, we prove a new sandwich theorem.
Ivan Singer +1 more
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DC Proximal Newton for Non-Convex Optimization Problems [PDF]
, 2015 We introduce a novel algorithm for solving learning problems where both the loss function and the regularizer are non-convex but belong to the class of difference of convex (DC) functions.
Flamary, Remi +2 more
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On the Co-Ordinated Convex Functions [PDF]
Applied Mathematics & Information Sciences, 2014 In this paper we established new integral inequalities which are more general results for coordinated convex functions on the coordinates by using some classical inequalities.
Ozdemir, M. Emin +2 more
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