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A differentiable path-following algorithm for computing perfect stationary points

Author

Listed:
  • Yang Zhan

    (City University of Hong Kong)

  • Peixuan Li

    (City University of Hong Kong)

  • Chuangyin Dang

    (City University of Hong Kong)

Abstract

This paper is concerned with the computation of perfect stationary point, which is a strict refinement of stationary point. A differentiable homotopy method is developed for finding perfect stationary points of continuous functions on convex polytopes. We constitute an artificial problem by introducing a continuously differentiable function of an extra variable. With the optimality conditions of this problem and a fixed point argument, a differentiable homotopy mapping is constructed. As the extra variable becomes close to zero, the homotopy path naturally provides a sequence of closely approximate stationary points on perturbed polytopes, and converges to a perfect stationary point on the original polytope. Numerical experiments are implemented to further illustrate the effectiveness of our method.

Suggested Citation

  • Yang Zhan & Peixuan Li & Chuangyin Dang, 2020. "A differentiable path-following algorithm for computing perfect stationary points," Computational Optimization and Applications, Springer, vol. 76(2), pages 571-588, June.
    • Handle: RePEc:spr:coopap:v:76:y:2020:i:2:d:10.1007_s10589-020-00181-3
    DOI: 10.1007/s10589-020-00181-3
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