An algorithm based on continuation techniques for minimization problems with highly non-linear equality constraints
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Publication:6325395
arXiv1909.07263MaRDI QIDQ6325395
A. Murua, Elisabete Alberdi, Mikel Antoñana, J. Makazaga
Publication date: 16 September 2019
Abstract: We present an algorithm based on continuation techniques that can be applied to solve numerically minimization problems with equality constraints. We focus on problems with a great number of local minima which are hard to obtain by local minimization algorithms with random starting guesses. We are particularly interested in the computation of minimal norm solutions of underdetermined systems of polynomial equations. Such systems arise, for instance, in the context of the construction of high order optimized differential equation solvers. By applying our algorithm, we are able to obtain 10th order time-symmetric composition integrators with smaller 1-norm than any other integrator found in the literature up to now.
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