Approximation with Convex Constraints

Abstract

This paper is a study of several problems of best approximation to a given function in a normed linear space from a convex subset of a finite-dimensional subspace. Specific problems treated are one-sided approximation and approximation with a positivity constraint, such as approximation by positive polynomials, monotonic polynomials or convex polynomials. Several new results are incorporated into a presentation of the previously known theory.