Polak-Ribiere conjugate gradient

Choose algorithm such as Steepest descent, Fletcher-Reeves (conjugate gradient), or Polak-Ribiere (conjugate gradient, default of FlyperChem), and choose options for termination condition such as RMS gradient (e.g., 0.1 kcal/mol A) or number of maximum cycles. 

The Polak-Ribiere conjugate gradient method " was used in RSll to perform the non-linear mnlhvariate optimization of the objective function with the weighing factors, Wj = 1 and W2 = 10. 

Points-On-a-Sphere (POS) force held, 39 Polak-Ribiere conjugate gradient optimization, 318 Polaiizabihty, 236, 248... 

Next choose Polak-Ribiere (conjugate gradient) as the algorithm with RMSG = 0.1 kcal/A-mole or maxi, cycles = 1000 as the termination condition twice... 

Inc., 2000, USA. The geometry optimizations used a Polak-Ribiere conjugated gradient algorithm for energy minimization in vacuum or water, with a final gradient of 0.1 kcal/A mol. The periodic box of water molecules comprises 216 water molecules in all calculations... 

HyperChem s optimizers (steepest descent, Fletcher-Reeves, and Polak-Ribiere conjugate-gradient methods, and the block diagonal Newton-Raphson) differ in their generality, convergence properties, and computational requirements. They are unconstrained optimization methods however, it is possible to restrain molecular mechanics and quantum mechanics calculations in HyperChem by adding extra restraining forces. 

IlyperChem supplies three types of optimi/ers or algorithms steepest descent, conjugate gradient (Fletcher-Reeves and Polak-Ribiere), and block diagonal (Newton-Raph son). 

HyperChem provides two versions of the conjugate gradient method, Fletcher-Reeves and Bolak-Rihiere. Polak-Ribiere is more refined and is the default eh oiee in HyperChem,... 

Several variants of the conjugate gradients method have been proposed. The formulatior given in Equation (5.7) is the original Fletcher-Reeves algorithm. Polak and Ribiere proposed an alternative form for the scalar constant 7) ... 

The Polak-Ribiere prescription is usually preferred in practice. Conjugate gradient methods have much better convergence characteristics than the steepest descent, but they are again only able to locate minima. They do require slightly more storage than the steepest descent, since the previous gradient also must be saved. 

Methods of this type are often known as conjugate gradient methods. Other examples are the Parian method19 and the method of Polak and Ribiere.20... 

In the Refinement step, the accepted test configurations generated from the previous Site-Search step wiU be minimized using the Polak-Ribiere non-Unear conjugate gradient algorithm (Press etal., 1988) with equation 1 (Hellinga Richards, 1991). 

An alternative formula for P, is the Polak-Ribiere formula see Leach, p. 225.) The idea of the conjugate-gradient method (which really should be called the conjugate-direction method) is to choose each new step in a direction that is conjugate to the directions used in the previous steps (where the word conjugate has a certain technical... 

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