Extreme Points in Convex Sets of Symmetric Matrices

Extreme Points in Convex Sets of Symmetric Matrices

This paper deals with the following problem: What are the extreme points of a convex set K of n X n matrices, which is the intersection of the set S„ of symmetric matrices of nonnegative type, with another convex subset of symmetric matrices HI In the case where the facial structure of H is known, we expose a general method to determine the extreme points of K (Theorem 1). Then, we apply this m...

Extreme Points of Polar Convex Sets

Approximating Extreme Points of Infinite Dimensional Convex Sets

The property that an optimal solution to the problem of minimizing a continuous concave function over a compact convex set in IRn is attained at an extreme point is generalized by the Bauer Minimum Principle to the infinite dimensional context. The problem of approximating and characterizing infinite dimensional extreme points thus becomes an important problem. Consider now an infinite dimensio...

POINTS FOR m-CONVEX SETS

Let S be closed, m-convex subset of R d S locally a full ddimensional, with Q the corresponding set of Inc points of S If q is an essential inc point of order k then for some neighborhood U of q Q u is expressible as a union of k or fewer (d2)-dimenslonal manifolds, each containing q For S compact, if to every q E Q there corresponds a k > 0 such that q is an essential inc point of order k then...

Extreme eigenvalues of real symmetric Toeplitz matrices

We exploit the even and odd spectrum of real symmetric Toeplitz matrices for the computation of their extreme eigenvalues, which are obtained as the solutions of spectral, or secular, equations. We also present a concise convergence analysis for a method to solve these spectral equations, along with an efficient stopping rule, an error analysis, and extensive numerical results.