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.Comment: 26 pages, 6 figures, 2 table