A differentiable path-following algorithm for computing perfect stationary points

Yang Zhan (), Peixuan Li () and Chuangyin Dang ()
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Yang Zhan: City University of Hong Kong
Peixuan Li: City University of Hong Kong
Chuangyin Dang: City University of Hong Kong

Computational Optimization and Applications, 2020, vol. 76, issue 2, No 9, 588 pages

Abstract: 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.

Keywords: Stationary point; Perfectness; Homotopy method; Path-following algorithm (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s10589-020-00181-3

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