Probability-One Homotopy Algorithms---How to Solve Hard Problems by Making Them Harder

Layne T. Watson, Virginia Polytechnic Institute and State University
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The theory for probability-one (also known as globally convergent) homotopy algorithms was developed in the 1970s, with software and broad application following in the remainder of the 20th century. Initially a mere curiosity, these algorithms evolved into a now standard tool in the nonlinear equation solving toolbox, and for some applications, are the preferred tool. The initial skepticism was partially due to the appearance that homotopy methods make hard problems even harder. This talk will sketch the theory, mathematical software, and applications of globally convergent homotopy algorithms.

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