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arXiv · 1603.00863

Optimization via Chebyshev Polynomials

Kareem T. Elgindy
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Abstract

This paper presents for the first time a robust exact line-search method based on a full pseudospectral (PS) numerical scheme employing orthogonal polynomials. The proposed method takes on an adaptive search procedure and combines the superior accuracy of Chebyshev PS approximations with the high-order approximations obtained through Chebyshev PS differentiation matrices (CPSDMs). In addition, the method exhibits quadratic convergence rate by enforcing an adaptive Newton search iterative scheme. A rigorous error analysis of the proposed method is presented along with a detailed set of pseudocodes for the established computational algorithms. Several numerical experiments are conducted on one- and multi-dimensional optimization test problems to illustrate the advantages of the proposed strategy.

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Kareem T. Elgindy. 2016-03-02. Optimization via Chebyshev Polynomials. https://doi.org/10.1007/s12190-016-1076-x

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