A modification of the penalty-barrier method of Breitfeld and Shanno is presented. The mathematical algorithm generates a sequence of simple bounded constrained subproblems, where the objective function is a logarithmic barrier function. The method and the corresponding algorithm are presented in detail. The global convergence of the algorithm is proved. The algorithm is implemented into a computer program (SPENBARB) in which the subproblems are solved by means of a simple bounded truncated Newton method. Compar isons between the Breitfeld-Shanno implementation, the SPENBAR package ( a sparse variant of PENBAR). and the SPENBARB package are provided. Preliminary numerical results show a significant improvement of this approach subject to the number of outer iterations, inner iterations, as well as of the execution time.
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