Another modified conjugate gradient coefficient with global convergence properties

Abstract

Conjugate gradient [CG] methods are considered in solving nonlinear unconstrained optimization problem, because of their simplicity, low memory requirement and global convergence properties. Different reviews and modification have been carried out in order to upgrade the method. In this paper, a new type of CG parameter, which satisfies the sufficient descent condition and global convergences property under exact line search, is proposed. The numerical outcomes indicate that our new modified parameter perform well when compare with other CG parameters for a given standards test function.

A new family of conjugate gradient coefficient with application

“…x y N  Under this assumption, we have the following lemma which was proven by [6]. This lemma also holds for the exact minimization rule, the Goldstein and the Wolfe rule as shown in [10].…”

Solving a large scale nonlinear unconstrained optimization problems by using new coefficient of conjugate gradient method with exact line search direction

“…The CPU processor used was Intel (R) Core TM i3-M350 (2.27GHz) with RAM 4 GB. (5,5), (20,20),(50,50) 8 TRECANNI 2 (5,5), (10,10),(50,50) 9 EXTENDED WOOD 4 (5,..,5), (20,..,20), (30,..,30) 10 CLOVILLE 4 (2,..,2),(4,..,4),(10,..,10) 11 HAGER 2 4 (7,7), (15,15),(22,) (7,..,7), (15,..,15), ( (15,15), (30,30),(150,150) (15,.,15), (30,..,30),(150,..,150) 16 EXTENDED PENALTY (1,1), (5,5),(10,10) (1,..,1),(5,..,5),(10,..,10) 23 EXTENDED TRIDIAGONAL1 2 10,100,1000 (6,6), (12,12),(17,17) (6,..,6), (12,..,12), (17,..,17) 24 DIAGONAL 4 2 10,100,1000…”

“…GENERRAL-IZED QUARTIC 2 10,100,1000 (7,7),(70,70),(140,140) (7,..,7),(70,..,70),(140,..,140) 30 QUADRATIC QF2 2 10,100,1000 (4,4), (16,16),(40,40) (4,..,4), (16,..,16),(40,..,40) 31 EXTENDED QUADRATIC PENALTY QP2 2 10,100,1000 (10,10), (20,20),(30,30) (10,..,10), (20,..,20), (30,..,30) 32 QUARTC 2 10,100,1000 (8,8), (16,16),(32,32) (8,..,8), (16,..,16),(32,..,32) 33 SUM SQUARES 2 10,100,1000…”

Another Modified DPRP Conjugate Gradient Method With Global Convergent Properties

“…where k β is a scalar, whose different form means various CG methods, some [12]. For their definition please see [28]. When the objective function is strictly convex quadratic function, all these methods under exact line search have the same convergence properties.…”

“…For which any given method is within a factor t of the best. For more detail please see [12] and [28]. In fact, in plotting the performance profiles, any top curved shaped of the algorithm is considered the best.…”