Towards optimal Newton-type methods for nonconvex smooth optimization Coralia Cartis Coralia.Cartis (at) ed.ac.uk School of Mathematics, Edinburgh University We show that the steepest-descent and Newton methods for unconstrained non-convex optimization, under standard assumptions, may both require a number of iterations and function evaluations arbitrarily close to the steepest-descent’s global...

An algorithm for gauge fixing to the minimal Landau gauge in lattice QCD is described. The method, a combination of an evolutionary algorithm with a steepest descent method, is able to solve the problem of the nonperturbative gauge fixing. The performance of the combined algorithm is investigated on 8, β = 5.7, and 16, β = 6.0, lattice SU(3) gauge configurations.

augmented downhill simplex method (adsm) is introduced here, that is a heuristic combination of downhill simplex method (dsm) with random search algorithm. in fact, dsm is an interpretable nonlinear local optimization method. however, it is a local exploitation algorithm; so, it can be trapped in a local minimum. in contrast, random search is a global exploration, but less efficient. here, rand...

We apply the method of nonlinear steepest descent to compute the long-time asymptotics of the Korteweg–de Vries equation for decaying initial data in the soliton and similarity region. This paper can be viewed as an expository introduction to this method.

In this paper we present a new steepest-descent type algorithm for convex optimization problems. Our algorithm pieces the unknown into sub-blocs of unknowns and considers a partial optimization over each sub-bloc. In quadratic optimization, our method involves Newton technique to compute the step-lengths for the sub-blocs resulting descent directions. Our optimization method is fully parallel a...

This paper proposes a new smart antenna beamforming scheme based on electronically steerable parasitic array radiator (ESPAR). The proposed method is capable of providing better capacity compared to the conventional ESPAR. The termination of each antenna element in this structure comprises a PIN diode in addition to a varactor. Using PIN diode besides the varactor provides more degrees of freed...

The effective and efficient numerical solution of Riemann–Hilbert problems has been demonstrated in recent work. With the aid of ideas from the method of nonlinear steepest descent for Riemann– Hilbert problems, the resulting numerical methods have been shown numerically to retain accuracy as values of certain parameters become arbitrarily large. The primary aim of this paper is to prove that t...