Greedy expansions in convex optimization

Greedy expansions in convex optimization

This paper is a follow up to the previous author’s paper on convex optimization. In that paper we began the process of adjusting greedytype algorithms from nonlinear approximation for finding sparse solutions of convex optimization problems. We modified there three the most popular in nonlinear approximation in Banach spaces greedy algorithms – Weak Chebyshev Greedy Algorithm, Weak Greedy Algor...

Greedy approximation in convex optimization

We study sparse approximate solutions to convex optimization problems. It is known that in many engineering applications researchers are interested in an approximate solution of an optimization problem as a linear combination of elements from a given system of elements. There is an increasing interest in building such sparse approximate solutions using different greedy-type algorithms. The prob...

Greedy Strategies for Convex Optimization

We investigate two greedy strategies for finding an approximation to the minimum of a convex function E defined on a Hilbert space H. We prove convergence rates for these algorithms under suitable conditions on the objective function E. These conditions involve the behavior of the modulus of smoothness and the modulus of uniform convexity of E.

Greedy expansions in Banach spaces

Greedy and Quasi-greedy Expansions in Non-integer Bases

We generalize several theorems of Rényi, Parry, Daróczy and Kátai by characterizing the greedy and quasi-greedy expansions in non-integer bases.