Secant Condition Free of a Spectral Wyl Conjugate Gradient (Cg) Method and Its Global Convergence Properties

Application of spectral conjugate gradient methods for solving unconstrained optimization problems

“…The comparisons are based on CPU time and number of iterations. The stopping criteria used is ‖g ‖ < where = 10 −6 as suggested by Hillstrom [21]. The set of standard test functions are considered from [1] and utilised with four different initial values.…”

“…‖g −1 ‖ 2 ≤ 2‖g ‖ 2 ‖g −1 ‖ 2 (6) where g and g −1 are gradient vectors at points , −1 respectively, and ‖. ‖ represent the Euclidian norm.…”

“…Compute by(5) and(6) Step 3: Compute by (11) and(12). If ‖g ‖ = 0, then stop.Step Compute by(3).Step Update the new point by the recurrence expression (2).…”

Descent Condition for a Scalar Parameter of Spectral HS (SpHS) Conjugate Gradient Method

“…The stopping criteria used for both methods is as recommended by [21] and . A benchmark problem functions in [8], [9], [10], [15] and [20] have used to established test problems in table 1 with four different initial points by MatlabR2015 subroutine programming using Intel® Core™ i5-3317U (1.7GHz with 4 GB (RAM)). In this paper, failure of the test function in each method is characterized due to (i) memory requirement (ii) number of iterations exceed 1000 (iii) CPU time running in seconds reaches 1000 (iv) Line search method failed to find the step size or step length (v) If is not a number (NaN).…”

“…Presently, [3] introduced a spectral CG method and computed their spectral parameter using the secant equation as originally given by [12]. Spectral CG method combines together the CG search direction and spectral parameter to construct a new search direction, see [1], [4], [8], [13], [14], [16], [17], [19], [20], [22] and [23], for the details. In this paper, we formulate the spectral parameter via the CG search direction and a scalar parameter of HS CG method.…”