Condition number based complexity estimate for computing local extrema |
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Authors: | Zhikun She Zhiming Zheng |
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Institution: | LMIB and School of Science, Beihang University, Beijing, China |
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Abstract: | In this paper, we present a new algorithm for computing local extrema by modifying and combining algorithms in symbolic and numerical computation. This new algorithm improves the classical steepest descent method that may not terminate, by combining a Sturm’s theorem based separation method and a sufficient condition on infeasibility. In addition, we incorporate a grid subdivision method into our algorithm to approximate all local extrema. The complexity of our algorithm is polynomial in a newly defined condition number, and singly exponential in the number of variables. |
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Keywords: | primary 68W40 secondary 68W30 |
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