Murtagh-Sargent method

Murtagh-Sargent method is locally and linearly convergent at x. ... 

T can be minimized in exactly the same fashion in which E itself was minimized, e.g., by using the Murtagh-Sargent or the BFGS procedure already described. A generalized Newton-Raphson method may also be employed, assuming... 

Murtagh B A and Sargent R W 1970 Computational experience with quadratically convergent minimisation methods Comput. J. 13 185... 

In 1967, Goldfarb 72 improved the method by using the projected gradients in Davidon s variable-metric formula to generate the steps. In 1968, Murtagh and Sargent 73 proposed a "variable-metric projection" version of Rosen s method, using the... 

Another technique for handling the mass balances was introduced by Castillo and Grossmann (1). Rather than convert the objective function into an unconstrained form, they implemented the Variable Metric Projection method of Sargent and Murtagh (32) to minimize Gibbs s free energy. This is a quasi-Newton method which uses a rank-one update to the approximation of H l, with the search direction "projected" onto the intersection of hyperplanes defined by linear mass balances. 

Analog computers may be employed in many ways in process engineering for the calculation of material and heat transfer processes [255]. In the last 10 years chiefh those methods have been further developed which can only be used by means of electronic computers [6]. These are, above all, the so-called matrix methods as evolved by Wang and Henke [256], Sargent and Murtagh [257] and Stainthorp et al. [258]. 

B. A. Murtagh and R. W. H. Sargent, Comput. J. 13 185 (1970) a principal disadvantage of this method is that for poor starting geometries it is plagued with resets. ... 

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