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A good introduction to optimization theory and a description of the the modern minimization techniques can be found in Gill, Murray and Wright [1]. Bard [2] deals with the particular problem of parameter estimation; chapters concerning the different estimators and their properties, and the interpretation of the estimates are remarkable. Updating formulas for Quasi--Newton methods are discussed in [4].
The reading of the cited chapters of [2] will allow an error--free interpretation of the results of the optimization algorithms. It is therefore recommended.
[1] Gill P.E., Murray W and Wright M.H. . Practical Optimization. Academic Press. London. 1981. [2] Bard Y. . Non--linear Parameter Estimation. Academic Press. London. 1974. [3] Gill P.E., Murray W. . Algorithms for the solution of non-linear least squares problems. SIAM J. of Num. An., vol 15, pp 977-992, 1978 [4] Gill P.E., Murray W. and Pitfield . The implementation of two revised algorithms for unconstrained optimization. Rep. NAC 11. Nat. Phys. 1972. Lab., Teddington. England.