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.
翻译:我们提出一种基于持续技术的算法,这种算法可以用来解决量化最小化的平等制约因素问题。我们侧重于大量当地微型项目的问题,这些问题很难通过局部最小化算法和随机的开始猜想获得。我们特别感兴趣的是计算多式方程式的确定不足的系统的最低标准解决方案。例如,在建造高排序优化差异方程解算器时,就会产生这种系统。通过应用我们的算法,我们能够获得第10级的时间对称构成集成器,比文献中迄今找到的任何其他集成器都小1个调。