A New Line-search Step Based on the Weierstrass }-function for Minimizing a Class of Logarithmic Barrier Functions
نویسندگان
چکیده
We deene the notion of self-concordance of order two for the restriction f of a logarithmic barrier function to a given line. Based on this notion we prove an inner approximation of the domain of f, as well as a lower bound of the distance from a point t to the minimum of f. These results provide the theoretical tools to develop a simple and eecient search step for nding the minimum of the barrier function along a given line. The new bound on the size of the line-search step is better than the optimal bound known for the case of a self-concordant function (of order one). We conclude with some numerical examples that illustrate the promise of the new line-search step.
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