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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Convex sets with Oka complements
Oka补 凸集 Oka流形
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2023/11/29
It is now known that the complement of any polynomially convex compact set K in C^n is an Oka manifold. In particular this holds if K is convex. I will discuss a recent result, joint with Forstneri?, ...
RATES OF CONVERGENCE FOR RANDOM APPROXIMATIONS OF CONVEX SETS
PACKING NUMBERS POLAR SET
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2015/8/20
The Hausdorff distance between a compact convex set K CRd and random sets
K c lRd iS studied. Basic inequalities are derived for the case of K being a convex
subset of K. If applied to special seq...
Lattice-point generating functions for free sums of convex sets
Lattice-point generating functions free sums of convex sets Combinatorics
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2012/7/11
Let $\J$ and $\K$ be convex sets in $\R^{n}$ whose affine spans intersect at a single rational point in $\J \cap \K$, and let $\J \oplus \K = \conv(\J \cup \K)$. We give expressions for the generating...
On super weakly compact convex sets and representation of {m swcc}(X)^*
super weakly compact set dual of normed semigroup uniform Fr'echet differetiability representation
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2011/10/20
In this note, we give first that a characterization of super weakly compact convex sets of a Banach space X, namely, a sufficient and necessary condition for a closed bounded convex set Ksubset X to b...
Algorithmic and Complexity Results for Cutting Planes Derived from Maximal Lattice-Free Convex Sets
Algorithmic and Complexity Results Maximal Lattice-Free Convex Sets Optimization and Control
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2011/9/20
Abstract: We study a mixed integer linear program with m integer variables and k non-negative continuous variables in the form of the relaxation of the corner polyhedron that was introduced by Anderse...
On affine maps on non-compact convex sets and some characterizations of finite-dimensional solid ellipsoids
affine maps non-compact convex sets characterizations of finite-dimensional solid ellipsoids
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2011/2/25
In recent studies, properties of the set of affine maps between two convex sets have been
investigated with intensive motivation from quantum physics, but in those preceding works
the underlying con...
Decompositions of Compact Convex Sets
Pairs of convex sets sublinear function quasidifferential calculus
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2009/2/5
In a recent paper R. Urbanski [13] investigated the mimimality of pairs compact convex sets which satisfy additional conditions, namely the minimal convex pairs. In this paper we consider some differe...
Invariants of Pairs of Compact Convex Sets
Pairs of convex sets sublinear function quasidifferential calculus
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2009/1/22
In a recent paper P. Diamond, P. Kloeden, A. Rubinov and A. Vladimirov [3] investigated comperative properties of three different metrics in the space of pairs of compact convex sets. These metrics de...
Least Deviation Decomposition with Respect to a Pair of Convex Sets
Least deviation decomposition convex analysis Moreau orthogonal decomposition
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2009/1/20
Let $K_1$ and $K_2$ be two nonempty closed convex sets in some normed space $(H,\Vert \cdot \Vert )$. This paper is concerned with the question of finding a "good" decomposition, with respect to $K_1$...
Compactly Epi-Lipschitzian Convex Sets and Functions in Normed Spaces
Convex Sets Compactly Epi-Lipschitzian Normed Spaces
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2009/1/15
We provide several characterizations of compact epi-Lipschitzness for closed convex sets in normed vector spaces. In particular, we show that a closed convex set is compactly epi-Lipschitzian if and o...
Inequalities for Lattice Constrained Planar Convex Sets
Planar Convex Set Lattice Lattice Point Enumerator Lattice-Point-Free Sublattice Area Perimeter Diameter Width Inradius Circumradius
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2008/7/1
Every convex set in the plane gives rise to geometric functionals such as the area, perimeter, diameter, width, inradius and circumradius. In this paper, we prove new inequalities involving these geom...
Inequalities for Planar Convex Sets
planar convex set inequality area perimeter diameter width inradius circumradius
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2008/7/1
This paper collects together known inequalities relating the area, perimeter, width, diameter, inradius and circumradius of planar convex sets. Also, a technique for finding new inequalities is stated...
Rate of Convergence of the Discrete Polya Algorithm from Convex Sets. A Particular Case
Best uniform approximation Rate of convergence Polya Algorithm Strong uniqueness
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2008/6/27
Rate of Convergence of the Discrete Polya Algorithm from Convex Sets. A Particular Case.
MODELLING RANDOM CONVEX SETS
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2007/8/7
A model is developed for convex-set valued data, which are the Minkowski sum of aconvex parameter set and a convex noise set. This model is generalized to include location and scale parameters. A furt...