Linearized Krylov subspace Bregman iteration with nonnegativity constraint

• DOI: 10.1007/s11075-020-01004-6
• Publication Date: 2020-09-07T17:02:55Z
• Authors: Alessandro Buccini; Mirjeta Pasha; Lothar Reichel
• Keywords: Krylov subspace; Theory of computation; Bregman divergence

Abstract Bregman-type iterative methods have received considerable attention in recent years due to their ease of implementation and the high quality computed solutions they deliver. However, these may require a large number iterations this reduces usefulness. This paper develops computationally attractive linearized Bregman algorithm by projecting problem be solved into an appropriately chosen low-dimensional Krylov subspace. The projection computational effort required for each iteration. A variant solution method, which nonnegativity iterate is imposed, also described. Extensive numerical examples illustrate performance proposed methods.