[PDF] Top 20 A Modified FR Conjugate Gradient Method with Strong Wolfe Line Search

... The rest of this paper is organized as follows. In the next section, a new MFR conjugate gradient Algorithm is proposed, some mild conditions are also given. In section3, we prove the global convergence of ... See full document

... the modified Fletcher-Reeves me- thod and modified Dai-Yuan ...the modified Fletcher-Reeves method is ...the modified Dai-Yuan method is employed, the excitation wavefront is not ... See full document

... PRP method has global convergence under Armijo line search technique for general functions but this fails for the Wolfe line ...the search direction that cannot be satisfied for ... See full document

... these line search approaches are well defined and have the advantage that they can guarantee the global convergence of the original PRP ...the strong Wolfe line search, they are ... See full document

... In other words, 𝐐 is guaranteed to be nearly orthogonal only when 𝐀 is a well-conditioned matrix. The CGS fails to satisfy the bound of equation (19) and the columns of 𝐐 may depart from orthogonality to an almost ... See full document

... three-term conjugate gradient ...three-term conjugate gradient method is based on Polak–Ribière–Polyak conjugate gradient ...Polak–Ribière–Polyak conjugate ... See full document

... were written in Matlab and run on a notebook computer with an Intel(R) Core(TM) i- U . GHz CPU, . GB of RAM and Linux operation system Ubuntu .. All test problems were drawn from the CUTEst test library ... See full document

... nonlinear conjugate gradi- ent methods such as Hestenes–Stiefel (HS) method [8], Fletcher–Reeves (FR) method [7], Polak–Ribiere–Polyak (PRP) method [20, 21], Dai–Yuan (DY) method ... See full document

... PRP method, which is generally believed to be the most efficient conjugate gradient methods, and has got meticulous in recent ...the method is that they essentially perform a restart if a bad ... See full document

... hybrid method combining the PRP method and the WYL ...hybrid method will possess some better properties of the PRP method and the WYL method: (i) the tendency to turn towards the ... See full document

... new conjugate gradient methods see 1, 13–16, 18, 19, 29, 30 which have good properties and good numerical ...the FR formula and the WYL formula, we only test Algorithm ...WWP line ... See full document

... the FR me- thod with different line ...PRP method may cycle and does not approach any stationary point even with exact line ...the FR method performs much worse than the PRP (HS, ... See full document

... modified conjugate gradient method to solve unconstrained optimization problems is proposed which satisfies the sufficient descent condition in the case of the strong Wolfe line ... See full document

... the conjugate gradient algorithm and obtained amazing ...jugate gradient algorithm is increasingly famous because of its simplicity and low require- ment of calculation ...good conjugate ... See full document

... The conjugate gradient method is a very useful technique for solving minimization problems and has wide applications in many ...new conjugate gradient methods by) for nonlinear ... See full document

... proposed method which would satisfied both the sufficient descent and the conjugacy ...DFP method, which is a quasi- Newton method belonging to the Broyden class ...The search direction in the ... See full document

... Consider the non linear equation g ( x )  0 whose one or more roots are to be found. y  g (x ) represents the graph of the function g (x ) and assume that an initial estimate x 0 is known for the desired root of the ... See full document

... the search directions obtained using (6) become linearly dependent after a few iterations of the above ...the search process becomes slow. In order to make the search faster, the linear dependence of ... See full document

... In this paper, we introduced seven alternative numerical algorithms for minimization of nonlinear unconstrained optimization problems and compared with Newton’s method. It is clear from the above numerical results ... See full document

... paper has the same results under weaker conditions. More dimension functions for practical problems are tested to show the performance of the modified algorithm and the normal algorithm. An application of the fact ... See full document