Polak

Polak E 1971 Computationai Methods in Optimization a Unified Approach (New York Academic)... 

Polak E 1997 Optimization Algorithms and Consistent Approximations (New York Springer)... 

Polak L S and Lebedev Yu A (ed) 998 Plasma C/rem/sfry (Cambridge Cambridge International Soienoe)... 

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) ... 

For quadratic functions this is identical to the Fletcher-Reeves formula but there is some evidence that the Polak-Ribiere may be somewhat superior to the Fletcher-Reeves procedure for non-quadratic functions. It is not reset to the steepest descent direction unless the energy has risen between cycles. 

E. Hala, 1. Wichtede, J. Polak, andT. Boubhk, Vapor—Eiquid Equilibrium at Normal Pressures Pergamon Press, Oxford, UK, 1968. 

There are several ways of choosing the /3 value. Some of the names associated with these methods are Fletcher-Reeves, Polak-Ribiere and Hestenes-Stiefel. Their definitions of /3 are... 

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. 

R.B. Bursel, Ispolsovanie plazmi v khimicheskikh processakh (Application of plasma in chemical processes) edited by L.S. Polak Mir, Moscow, 1970 (in Russian). 

Annemarie Polak F. Hoffmann-La Roche Ltd Aesch, Basel Switzerland... 

Owing to the constraints, no direct solution exists and we must use iterative methods to obtain the solution. It is possible to use bound constrained version of optimization algorithms such as conjugate gradients or limited memory variable metric methods (Schwartz and Polak, 1997 Thiebaut, 2002) but multiplicative methods have also been derived to enforce non-negativity and deserve particular mention because they are widely used RLA (Richardson, 1972 Lucy, 1974) for Poissonian noise and ISRA (Daube-Witherspoon and Muehllehner, 1986) for Gaussian noise. 

Schwartz, A., Polak, E., 1997, Family of projected descent methods for optimization problems with simple bounds. Journal of Optimization Theory and Applications 92, 1... 

E. Polak, Computational Methods in Optimization, vol. 77 of Mathematics in Science and engineering, Academic Press New York, 1971. 

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