Homotopy continuation methods for computer-aided process design☆
Homotopy continuation methods for computer-aided process design☆
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DOI：
10.1016/0098-1354(87)80002-9
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发表时间：
1987
影响因子：
4.3
通讯作者：
T. L. Wayburn;J. Seader
中科院分区：
文献类型：
--
作者：
T. L. Wayburn;J. Seader
同伦连续方法已被作者和其他人用来解决困难的化学工程流程和设计问题，涉及到联立非线性方程组的解决方案。在以下情况下，这些方法可能会失败：（1）从简单问题的解到原始（困难）问题的解所遵循的同伦路径返回到简单问题的第二个解;（2）同伦路径到达原始（向量值）函数的定义域的内边界;以及（3）同伦路径走向无穷远。对于前两种模式的故障，使用仿射同伦在这里讨论作为一种可能的补救措施。由无界同伦路径引起的失效是当前研究的主题。
Homotopy continuation methods have been used by the authors and others to solve difficult chemical engineering flowsheeting and design problems involving the solution of simultaneous nonlinear equations. Such methods can fail when: (1) the homotopy path, which one follows from the solution of a simple problem to the solution of the original (difficult) problem, returns to a second solution of the simple problem; (2) the homotopy path strikes an interior boundary of the domain of definition of the original (vector-valued) function; and (3) the homotopy path goes off to infinity. For the first two modes of failure, the use of an affine homotopy is discussed here as a possible remedy. Failure due to an unbounded homotopy path is the subject of current research.