Local min-orthogonal principle and its applications for solving multiple solution problems

Abstract

In this article we establish a double-orthogonal principle, and a local min-orthogonal method with its step size rule, and its convergence under assumptions more general than those in its previous versions. With such a general framework, we justify mathematically the two new  algorithms proposed for solving W-type problems. Numerical examples for finding multiple solutions to W-type and to mixed M-W-type problems illustrate the flexibility of this method. See also