Semidefinite programming for optimizing convex bodies under width constraints
نویسندگان
چکیده
منابع مشابه
Semidefinite programming for optimizing convex bodies under width constraints
We consider the problem of minimizing a functional (like the area, perimeter, surface) within the class of convex bodies whose support functions are trigonometric polynomials. The convexity constraint is transformed via the Fejér-Riesz theorem on positive trigonometric polynomials into a semidefinite programming problem. Several problems such as the minimization of the area in the class of cons...
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In this article, we introduce a new concept of general mixed width-integral of convex bodies, and establish some of its inequalities, such as isoperimetric inequality, Aleksandrov-Fenchel inequality, and cyclic inequality. We also consider the general width-integral of order i and show its related properties and inequalities. c ©2016 All rights reserved.
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is isotropic with respect to an appropriate measure depending on f . The purpose of this note is to provide applications of this point of view in the case of the mean width functional T 7→ w(TK) under various constraints. Recall that the width of K in the direction of u ∈ Sn−1 is defined by w(K,u) = hK(u) + hK(−u), where hK(y) = maxx∈K〈x, y〉 is the support function of K. The width function w(K,...
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ژورنال
عنوان ژورنال: Optimization Methods and Software
سال: 2012
ISSN: 1055-6788,1029-4937
DOI: 10.1080/10556788.2010.547580