A new class of nonlinear conjugate gradient coefficients with global convergence properties

A class of new derivative-free gradient type methods for large-scale nonlinear systems of monotone equations

“…For unconstrained optimization problem, Rivaie et al [11] designed a RMIL conjugate gradient method. Fang and Ni [6] extended the RMIL method to solve large-scale nonlinear systems of equations with the ideas of nonmonotone line search.…”

“…For systems of monotone equations, we describe a class of new derivative-free gradient type method, which is inspired by the efficiency of the RMIL method [11], and the strategy of projection method [12]. This paper is organized as follows.…”

A New Parameter Conjugate Gradient Method Based on Three Terms Unconstrained Optimization

“…normally the s earch direction at the fi rst iteration is the steepest descent direction , namely 1 = − 1 and the other search directions can be defined as: +1 = − +1 + (1.3) Where = ∇ ( ) and is a scalar. There are many formulas for , for example, Hestenes-Stiefel (HS) [ 8] , Conjugate descent (CD ) [10], Polak-Ribi ere-Polyak (PRP) [1] , Dai and Yuan (DY) [11] , (D PRP) [2] , RMIL [9] and 1 [12], these formulas are as follows:…”

A modification of steepest descent method for solving large-scaled unconstrained optimization problems

“…In the steepest descent method [1], the search direction, k d , is defined as the negative gradient direction kk dg  (2) and the most common line search for determining the step length is the exact line search, which is 0 min ( )…”

“…In recent years, we have discovered an enlarging number of studies adopting the exact line search due to the new era of faster computer processors such as [2][3][4]. Different search directions correspond to different iterative methods.…”