On initial point selection of the steepest descent algorithm for general quadratic functions

Masoud Fatemi ()
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Masoud Fatemi: K. N. Toosi University of Technology

Computational Optimization and Applications, 2022, vol. 82, issue 2, No 2, 329-360

Abstract: Abstract We prove some new results about the asymptotic behavior of the steepest descent algorithm for general quadratic functions. Some well-known results of this theory are developed and extended to non-convex functions. We propose an efficient strategy for choosing initial points in the algorithm and show that this strategy can dramatically enhance the performance of the method. Furthermore, a modified version of the steepest descent algorithm equipped with a pre-initialization step is introduced. We show that an initial guess near the optimal solution does not necessarily imply fast convergence. We also propose a new approach to investigate the behavior of the method for non-convex quadratic functions. Moreover, some interesting results about the role of initial points in convergence to saddle points are presented. Finally, we investigate the probability of divergence for uniform random initial points.

Keywords: Steepest descent method; Saddle points; Initial point strategy; Asymptotic analysis; 90C06; 90C26; 65Y20 (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s10589-022-00372-0

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