ABSTRACT
This chapter summarizes the basic theory of globally convergent homotopy methods relevant to engineering analysis, describes a parallel homotopy algorithm and some available computer software, and gives some actual engineering applications. It provides an intuitive explanation of what is different about the new globally convergent homotopy algorithms, and briefly recounts the basic mathematical theory. The chapter outlines some numerical algorithms implemented in the mathematical software package HOMPACK. It describes a parallel homotopy algorithm. The chapter provides examples of the globally convergent homotopy techniques applied to engineering. Homotopy algorithms for convex unconstrained optimization are only of theoretical interest, and are generally not computationally competitive with other approaches, but it is reassuring that the globally comvergent homotopy techniques can theoretically be directly applied. The homotopy algorithm is to track the d curves, which contain all isolated zeros of the polynomial system.
