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An Adaptive Procedure for the Global Minimization of a Class of Polynomial Functions

Istituto di Informatica e Telematica (IIT–CNR), Via G. Moruzzi 1, 56124 Pisa, Italy
Dipartimento di Matematica, University of Parma, Parco Area delle Scienze 53/A, 43124 Parma, Italy
Dipartimento di Informatica, University of Pisa, Largo Pontecorvo 3, 56127 Pisa, Italy
Author to whom correspondence should be addressed.
Algorithms 2019, 12(5), 109;
Received: 15 April 2019 / Revised: 16 May 2019 / Accepted: 20 May 2019 / Published: 23 May 2019
PDF [438 KB, uploaded 23 May 2019]


The paper deals with the problem of global minimization of a polynomial function expressed through the Frobenius norm of two-dimensional or three-dimensional matrices. An adaptive procedure is proposed which applies a Multistart algorithm according to a heuristic approach. The basic step of the procedure consists of splitting the runs of different initial points in segments of fixed length and to interlace the processing order of the various segments, discarding those which appear less promising. A priority queue is suggested to implement this strategy. Various parameters contribute to the handling of the queue, whose length shrinks during the computation, allowing a considerable saving of the computational time with respect to classical procedures. To verify the validity of the approach, a large experimentation has been performed on both nonnegatively constrained and unconstrained problems. View Full-Text
Keywords: global minimization; polynomial function; adaptive strategy global minimization; polynomial function; adaptive strategy

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Favati, P.; Lotti, G.; Menchi, O.; Romani, F. An Adaptive Procedure for the Global Minimization of a Class of Polynomial Functions. Algorithms 2019, 12, 109.

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