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Lemma 1.8.2 - Convex Bodies: The Brunn-Minkowski Theory

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#metric-spaces #proof-explanation #convex-geometry
49
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Why does one of the following constraints define a convex set while another defines a non-convex set?

Published on
#convex-analysis #convex-geometry
130
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Is the logarithm of Banach-Mazur distance between convex bodies an actual distance?

Published on
#convex-geometry
40
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Convex set in $\mathbb{R}^2_+$

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#analysis #convex-analysis #convex-optimization #convex-geometry
69
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Unit-length 2D curve segment with maximal width along all directions

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#geometry #optimization #euclidean-geometry #convex-geometry #convex-hulls
77
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A point in a convex hull

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#convex-analysis #convex-geometry #convex-hulls
328
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Geometric proof of Caratheodory's theorem

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#convex-geometry
96
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The permutations of (1,1,0,0), (-1,1,0,0), (-1,-1,0,0) are vertices of a polytope.

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#polytopes #discrete-geometry #convex-geometry
1.4k
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Computing the subgradient of an indicator function or the normal cone of a set

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#convex-analysis #convex-optimization #convex-geometry
82
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3 Dimensional space

Published on
#geometry #euclidean-geometry #convex-geometry
175
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An example of a set of points in $R^3$ which is not open, not closed, not convex and not bounded

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#convex-analysis #convex-geometry
48
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Interpreting nonnegativity of inner product in multiple dimensions

Published on
#real-analysis #convex-analysis #convex-geometry
298
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Convex combination of $2^n$ vectors from cartesian products of half-spaces

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#combinatorics #convex-analysis #convex-geometry #convex-hulls
148
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Prove that a set $A$ is convex $(x+y)A = xA + yA$

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#algebraic-geometry #convex-geometry
42
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Equivalent formulation of convex functions

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#optimization #convex-analysis #convex-geometry

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