Some comments on floating and centroid bodies in the plane
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DOI: 10.1007/s00010-017-0525-4
Abstract: Consider a long, convex, homogenous cylinder with horizontal axis and with a planar convex body K as transversal section. Suppose the cylinder is immersed in water and let $$K_w$$Kw be the wet part of K.… read more here.
Keywords: bodies plane; centroid bodies; floating centroid; convex ... See more keywords
Lattice-equivalence of convex spaces
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DOI: 10.1007/s00012-019-0600-x
Abstract: The links between order and topology have been extensively studied. The objective of this paper is to study the similar links between convex spaces and order structures via the lattices of convex sets. In particular,… read more here.
Keywords: convex spaces; topology; equivalence convex; convex ... See more keywords
On the Raşa Inequality for Higher Order Convex Functions
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DOI: 10.1007/s00025-021-01417-2
Abstract: We study the following $$(q-1)$$ th convex ordering relation for qth convolution power of the difference of probability distributions $$\mu $$ and $$\nu $$ $$\begin{aligned} (\nu -\mu )^{*q}\ge _{(q-1)cx} 0 , \quad q\ge 2, \end{aligned}$$… read more here.
Keywords: order convex; inequality; higher order; convex functions ... See more keywords
Noncommutative Polynomials Describing Convex Sets
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DOI: 10.1007/s10208-020-09465-w
Abstract: The free closed semialgebraic set $${\mathcal {D}}_f$$ D f determined by a hermitian noncommutative polynomial $$f\in {\text {M}}_{{\delta }}({\mathbb {C}}\mathop {})$$ f ∈ M δ ( C < x , x ∗ > ) is… read more here.
Keywords: closed semialgebraic; free closed; convex; mathop ... See more keywords
A proximal difference-of-convex algorithm with extrapolation
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DOI: 10.1007/s10589-017-9954-1
Abstract: We consider a class of difference-of-convex (DC) optimization problems whose objective is level-bounded and is the sum of a smooth convex function with Lipschitz gradient, a proper closed convex function and a continuous concave function.… read more here.
Keywords: difference convex; dca; extrapolation; convex ... See more keywords
Nonclassical Probability and Convex Hulls
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DOI: 10.1007/s10670-016-9807-9
Abstract: AbstractIt is well known that the convex hull of the classical truth value functions contains all and only the probability functions. Work by Paris and Williams has shown that this also holds for various kinds… read more here.
Keywords: convex hulls; probability; nonclassical probability; convex ... See more keywords
Globally minimizing the sum of a convex–concave fraction and a convex function based on wave-curve bounds
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DOI: 10.1007/s10898-019-00870-2
Abstract: We consider the problem of minimizing the sum of a convex–concave function and a convex function over a convex set (SFC). It can be reformulated as a univariate minimization problem, where the objective function is… read more here.
Keywords: convex concave; sum convex; convex; curve bounds ... See more keywords
Exact Lipschitz Regularization of Convex Optimization Problems
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DOI: 10.1007/s10957-024-02465-8
Abstract: We consider the class of convex composite minimization problems which consists of minimizing the sum of two nonsmooth extended valued convex functions, with one which is composed with a linear map. Convergence rate guarantees for… read more here.
Keywords: regularization convex; convex; regularization; exact lipschitz ... See more keywords
Gaussian Convex Bodies: a Nonasymptotic Approach
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DOI: 10.1007/s10958-019-04256-3
Abstract: We study linear images of a symmetric convex body C ⊆ ℝN under an n × N Gaussian random matrix G, where N ≥ n. Special cases include common models of Gaussian random polytopes and… read more here.
Keywords: geometry; bodies nonasymptotic; nonasymptotic approach; gaussian convex ... See more keywords
Maps with the Radon–Nikodým Property
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DOI: 10.1007/s11228-017-0428-5
Abstract: We study dentable maps from a closed convex subset of a Banach space into a metric space as an attempt of generalize the Radon-Nikodým property to a “less linear” frame. We note that a certain… read more here.
Keywords: banach space; space; radon nikod; convex ... See more keywords
SOS-Convex Semialgebraic Programs and its Applications to Robust Optimization: A Tractable Class of Nonsmooth Convex Optimization
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DOI: 10.1007/s11228-017-0456-1
Abstract: In this paper, we introduce a new class of nonsmooth convex functions called SOS-convex semialgebraic functions extending the recently proposed notion of SOS-convex polynomials. This class of nonsmooth convex functions covers many common nonsmooth functions… read more here.
Keywords: class nonsmooth; sos convex; convex; optimization ... See more keywords