Show that the set is convex if and only if its intersection with any line is convex. Show that the convex hull of the $S$ set is the intersection of all convex sets ...
CONVEXITY OF LEVEL SETS FOR ELLIPTIC PROBLEMS IN CONVEX DOMAINS OR CONVEX RINGS: TWO COUNTEREXAMPLES
American Journal of Mathematics, Vol. 138, No. 2 (April 2016), pp. 499-527 (29 pages) This paper deals with some geometrical properties of solutions of some semilinear elliptic equations in bounded ...
Convex geometry and point set configurations form a pivotal area of research in computational geometry, where the primary focus is the study of convex sets and the intricate arrangements of points in ...
The Annals of Probability, Vol. 3, No. 3 (Jun., 1975), pp. 503-515 (13 pages) Let $X_1, X_2, \cdots$ be i.i.d. random vectors in $R_k$. Let $P_n$ denote the ...
Abstract: The concave-convex procedure (CCCP) is an iterative algorithm that solves d.c. (difference of convex functions) programs as a sequence of convex programs. In machine learning, CCCP is ...
Abstract: A portfolio optimization problem is a convex optimization problem that involves a linear objective function with quadratic constraints. One method for solving portfolio optimization problems ...
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