In this paper, an unconstrained minimization algorithm is defined in which a nonmonotone line search technique is employed in association with a truncated Newton algorithm. Numerical results obtained for a set of standard test problems are reported which indicate that the proposed algorithm is highly effective in the solution of illconditioned as well as of large dimensional problems.

In this paper we provide implementable methods for solving nondifferentiable convex optimization problems. A typical method minimizes an approximate Moreau–Yosida regularization using a quasi-Newton technique with inexact function and gradient values which are generated by a finite inner bundle algorithm. For a BFGS bundle-type method global and superlinear convergence results for the outer ite...

In this paper we perform a numerical study of Newton polynomial interpolation. We explore the Leja ordering of Chebyshev knots and the Fast Leja knots introduced by Reichel. In all previous publications we are aware of, the degree of interpolation polynomials in use is in the order of a few hundreds. We show that it is possible to employ degrees of up to one million or higher without a numerica...

Let T be a Jordan curve in the complex plane, and let Í) be the compact set bounded by T. Let / denote a function analytic on O. We consider the approximation of / on fî by a polynomial p of degree less than n that interpolates / in n points on T. A convenient way to compute such a polynomial is provided by the Newton interpolation formula. This formula allows the addition of one interpolation ...

Let K be a field. Generalizing the binomial coefficient polynomials ( X n ) , the Newton interpolation basis polynomials relative to an infinite sequence a = (ai)i=0 of distinct elements of K are defined by [X n ] a = ∏n−1 i=0 X−ai an−ai ∈ K[X ]. There is a complete and natural set of relations for these polynomials, namely, [X m ] a [X n ] a = ∑m+n l=max(m,n)[m,n, l]a [X l ] a , where the coef...

The humanoid robot garners paramount interest because of its ability to mimic human-like behavior in real-time environments. In this paper, a hybridized Artificial Potential Field (APF)-Broyden Fletcher Goldfarb Shanno (BFGS) Quasi-Newton technique is being proposed for the trajectory planning robot. methodology combines faster local search BFGS method with global APF an efficient and faster-hy...