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On local non-global minimizers of quadratic functions with cubic regularization

Andrea Cristofari(cristofari***at***dis.uniroma1.it)
Tayebeh Dehghan Niri(mathtd18175***at***yahoo.com)
Stefano Lucidi(lucidi***at***dis.uniroma1.it)

Abstract: In this paper, we analyze some theoretical properties of the problem of minimizing a quadratic function with a cubic regularization term, arising in many methods for unconstrained and constrained optimization that have been proposed in the last years. First we show that, given any stationary point that is not a global solution, it is possible to compute, in closed form, a new point with a smaller objective function value. Then, we prove that a global minimizer can be obtained by computing a finite number of stationary points. Finally, we extend these results to the case where stationary conditions are satisfied approximately, discussing some possible algorithmic applications.

Keywords: Unconstrained optimization. Cubic regularization. Global minima.

Category 1: Nonlinear Optimization (Unconstrained Optimization )


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Entry Submitted: 11/28/2017
Entry Accepted: 11/28/2017
Entry Last Modified: 11/28/2017

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