Biorthogonal Greedy Algorithms in convex optimization

The study of greedy approximation in the context convex optimization is becoming a promising research direction as algorithms are actively being employed to construct sparse minimizers for functions with respect given sets elements. In this paper we propose unified way analyzing certain kind greedy-type minimization on Banach spaces. Specifically, define class Weak Biorthogonal Greedy Algorithms that contains wide range algorithms. We analyze introduced and establish properties convergence, rate numerical stability, which understood sense steps algorithm allowed be performed not precisely but controlled computational inaccuracies. show following well-known — Chebyshev Algorithm (co) Free Relaxation belong class, introduce new Rescaled Relaxed (co). Presented experiments demonstrate practical performance aforementioned setting compared regularization, conventional approach constructing minimizers.