An approximate gradient-type method for nonlinear symmetric equations with convex constraints

Abstract

Based on the projection operator and the pseudo-monotone property, an approximate gradient-type method is proposed to solve nonlinear symmetric equations with convex constraints. The proposed method does not need any precise gradient or Jacobian matrix information, and only uses some approximate substitutions based on the symmetric property of equations. Under some appropriate assumptions, the global convergence and R-linear convergence rate are proved. Numerical experiments show that the proposed method is stable and effective for the test problems.