Convexity and Optimization in Finite Dimensions I

TL;DR: This work provides results which allow one to “calculate” the linear relaxation of a composite construction, in terms of set operations on the relaxation of the base sets, and compares the size of the relaxations for different formulations of the same MIP set.

TL;DR: In this paper, the authors study the problem of estimating a location vector restricted to a convex cone when the dimension, p, is at least 3 and find estimators which improve on the MLE in the normal case in the general case of a spherically symmetric distribution with unknown scale.

TL;DR: In this article, a separating-hyperplane algorithm for finding a nearest pair of points in two polytopes, where each polytope is expressed as the convex hull of given points in a Euclidian space, is proposed.

TL;DR: In this paper, it was shown that an upper semicontinuous quasiconvex functional over a compact (possibly nonconvex) subset K of a real Hausdorff locally convex space E is directionally monotone.