Convex optimization uiuc

In Section 3 we present a fast scheme for minimizing smooth convex functions

One of the advantages of this scheme consists in a possibility to use a specific norm, which is suitable for measuring the curvature of a particular objective function

This ability is similar to that of the mirror descent methods [8, 1]

Historically, the subgradient methods were the first numerical schemes for non-smooth convex minimization (see and for historical comments)

Very soon it was proved that the efficiency estimate of these schemes is of the order is the desired absolute accuracy of the approximate solution in function value (see also )

Convex optimization Convex optimization seeks to minimize a convex function over a convex (constraint) set

When the constraint set consists of an entire Euclidean space such problems can be easilysolved by classical Newton-type methods, and we have nothing to say about these uncon-strained problems