基于延拓技术的高度非线性等式约束极小化问题的算法
An algorithm based on continuation techniques for minimization problems with highly non-linear equality constraints
摘要：
我们提出了一个算法的基础上延续技术，可应用于解决数值最小化问题的等式约束。我们专注于大量的局部极小值的问题，这是很难获得的局部极小化算法与随机开始猜测。我们对多项式方程的欠定组的极小范数解的计算特别感兴趣。例如，这种系统出现在高阶优化的微分方程求解器的构造的上下文中。通过应用我们的算法，我们能够获得10阶时间对称的复合积分器具有较小的1-范数比任何其他的积分器中发现，到目前为止。
英文摘要：
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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