Convexity and Optimization in Finite Dimensions I

TL;DR: In this article, the authors generalized the technique of partitioning Rn into disjoint regions to bounds based on arbitrary polyhedral cones, which they used to find confidence bounds in regression analysis.

TL;DR: In this paper, a dual primal algorithm for finding the minimum norm point in the convex hull of a given finite set of points in a Euclidean space is presented, which is closely related to P. Wolfe's primal algorithm which finds a.equence of norm-decreCing points in the given polytope.

TL;DR: In this paper, a set of generators for a polyhedral cone is found by using a new representation for the polar (dual) cone, and examples from order-restricted statistical inference are chosen to illustrate this method.

TL;DR: In this article, the optimal return function is shown to be convex and the admissible control region is assumed to be a continuous function of the (perfectly) observed state, and the optimal feedback controls are shown to exist within the class of Borel measurable functions of past states.