Parallel tangents and steepest descent optimization algorithm-a computer implementation with application to linear, partially linear models and qualitative data†

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Abstract
This paper presents a computer implementation of the “partan” and steepest descent optimization algorithms. Some ideas on fitting partially linear models and maximum likelihood estimation of linear or nonlinear models with variance-covariance matrix depending on the parameters are also reported. Section 1 gives an introduction to the partan and steepest descent optimization algorithms. Section 2 describes problems solvable by the present routine. Section 3 presents an analysis of the program and, in particular, treats the problem of line minimization. A documentation of the program is given in Section 4. Results of test problems are given in Section 5. The fitting of nonlinear models is discussed in Section 6. Finally, the use of the present routine for the maximum likelihood estimation of linear and nonlinear models with variance structure depending on the unknown parameters is presented in Section 7. Special attention is paid to the analysis of rndtidirnensionai contingency tables.