Abstract
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.
Highlights
Global optimization over continuous spaces is an important field of the modern scientific research and involves interesting aspects in computer science
In this paper we propose an adaptive strategy for finding the global minimum of a polynomial function expressed through the Frobenius norm of matrices and tensors
In this paper an adaptive strategy, called AD, has been introduced for finding the global minimum of a polynomial function expressed through the Frobenius norm of matrices and tensors
Summary
Global optimization over continuous spaces is an important field of the modern scientific research and involves interesting aspects in computer science. Search algorithms [1], where an extensive sampling of independent points is considered, and Multistart algorithms [2,3], which apply local optimizers to randomly generated starting points; the best among the found local optima is considered the global optimum. Various methods are devised for escaping from an already found local optimum, reaching other feasible points from which to restart a new local optimizer (see for example the Simulated Annealing [4]). It implements a tailored local minimization procedure with an ad-hoc stopping condition.
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