An adaptive family of projection methods for constrained monotone nonlinear equations with applications

摘要

An adaptive class of conjugate gradient methods is proposed in this paper, which all possess descent property under strong-wolfe line search. The adaptive parameter in the search direction is determined by minimizing the distance between relative matrix and self-scaling memoryless BFGS update by Oren in the Frobenius norm. Two formulas of the adaptive parameter are further obtained, which are presented as those given by Oren and Luenberger (1973/74) and respectively Oren and Spedicato (1976). By projection technology, two adaptive projection algorithms are developed for solving monotone nonlinear equations with convex constraints. Some numerical comparisons show that these two algorithms are efficient. Last, the proposed algorithms are used to recover a sparse signal from incomplete and contaminated sampling measurements; the results are promising.