Recently, conjugate gradient methods, which usually generate descent search directions, are useful for large-scale optimization. Narushima et al. (SIAM J Optim 21:212–230, <CitationRef CitationID="CR22">2011</CitationRef>) have proposed a three-term conjugate gradient method which satisfies a sufficient descent condition. We extend this...</citationref>

In this paper we consider the problem of minimizing a smooth function by using the adaptive cubic regularized (ARC) framework. We focus on the computation of the trial step as a suitable approximate minimizer of the cubic model and discuss the use of matrix-free iterative methods. Our approach...

Based on some new interpolation conditions, a quadratic interpolation model is constructed to approximate the objective function, and then a class of modified BFGS methods with function value information is presented. The new methods satisfy some new weak secant equations and there is a...