A modified Dai–Yuan method with restart mechanism for nonlinear system of equations with a signal recovery

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The Dai--Yuan method is an important iterative scheme for solving unconstrained optimization problems, but it often requires exact or Wolfe-type line searches to satisfy descent or sufficient descent conditions. It may also perform poorly due to the jamming phenomenon. This paper presents a modified three-term Dai--Yuan method for solving constrained systems of nonlinear monotone equations. The search direction of the proposed method includes a nonnegative parameter whose value is determined through singular-value analysis of the iteration matrix. The method also incorporates a restart mechanism that ensures global convergence regardless of the line-search procedure used. Theoretical analysis establishes the global convergence and convergence rate of the proposed scheme under suitable assumptions. Numerical experiments on constrained nonlinear equations and sparse signal reconstruction demonstrate the efficiency of the method compared with related algorithms.

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