Nearly convex sets: fine properties and domains or ranges of subdifferentials of convex functions [PDF]
arXiv, 2015 Nearly convex sets play important roles in convex analysis, optimization and theory of monotone operators. We give a systematic study of nearly convex sets, and construct examples of subdifferentials of lower semicontinuous convex functions whose domain or ranges are nonconvex.
arxiv
Compact convex sets that admit a lower semicontinuous strictly convex function [PDF]
arXiv, 2015 We study the class of compact convex subsets of a topological vector space which admits a strictly convex and lower semicontinuous function. We prove that such a compact set is embeddable in a strictly convex dual Banach space endowed with its weak$^*$ topology.
arxiv
Qualitative analysis of basic notions in parametric convex programming. II. Parameters in the objective function [PDF]
, 1977 M.S. Osman
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About properties of the mean value functional and of the continuous infimal convolution in stochastic convex analysis [PDF]
, 1976 Hiriart-Urruty Jean-Baptiste
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The use of conjugate convex functions in complex analysis [PDF]
, 1983 Christer Kieselman
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On Jensen Functional, Convexity and Uniform Convexity [PDF]
arXivIn this paper we improve results related to Normalized Jensen Functional for convex functions and Uniformly Convex Functions.
arxiv
Remarks on the $Γ$-regularization of Non-convex and Non-semi-continuous Functions on Topological Vector Spaces [PDF]
Journal of Convex Analysis 19(2):467-483 (2012), 2016 We show that the minimization problem of any non-convex and non-lower semi-continuous function on a compact convex subset of a locally convex real topological vector space can be studied via an associated convex and lower semi-continuous function $\Gamma \left( h\right) $. This observation uses the notion of $\Gamma $-regularization as a key ingredient.
arxiv
Convex analysis and ideal tensegrities
Comptes Rendus. Mécanique, 2011 Abstract A theoretical framework based on convex analysis is formulated and developed to study tensegrity structures under steady-state loads. Many classical results for ideal tensegrities are rationally deduced from subdifferentiable models in a novel mechanical perspective. Novel energy-based criteria for rigidity and pre-stressability are provided,
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New integral inequalities via $(α,m)$-convexity and quasi-convexity [PDF]
arXiv, 2012 In this paper, we establish some new integral inequalities for $(\alpha, m)-$convex functions and quasi-convex functions, respectively. Our results in special cases recapture known results.
arxiv
arXiv, 2012 In this paper, one new classes of convex functions which is called MT-convex functions are given. We also establish some Hadamard-type inequalities.
arxiv