Abstract
In this paper, we propose a modified Polak–Ribière–Polyak (PRP) conjugate gradient method for solving large-scale nonlinear equations. Under weaker conditions, we show that the proposed method is globally convergent. We also carry out some numerical experiments to test the proposed method. The results show that the proposed method is efficient and stable.
Highlights
Solving nonlinear equations is an important problem which appears in various models of science and engineering such as computer vision, computational geometry, signal processing, computational chemistry, and robotics
The subproblems in the generalized proximal algorithms with Bergman distances is a monotone nonlinear equations [1], and l1-norm regularized optimization problems can be reformulated as monotone nonlinear equations [2]
We are interested in the numerical methods for solving monotone nonlinear equations with convex constraints: F(x) 0, x ∈ S, (1)
Summary
Solving nonlinear equations is an important problem which appears in various models of science and engineering such as computer vision, computational geometry, signal processing, computational chemistry, and robotics. We are interested in the numerical methods for solving monotone nonlinear equations with convex constraints: F(x) 0, x ∈ S,. If there is a convex function f(x) satisfying ∇f(x) F(x), solving the optimization problems (3) is equivalent to solving monotone nonlinear equations (1). A natural idea to solve monotone nonlinear equations (1) is to use the existing efficient methods for solving optimization problems (3). We combined the projection method [3], the modified nonlinear PRP conjugate gradient method for unconstrained optimization [20] and the iterative method [10] and proposed a modified nonlinear conjugate gradient method for solving large-scale nonlinear monotone equations with convex constrains. We use the proposed methods to solve practical problems in compressed sensing
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