In this chapter, we investigate recently proposed nonlinear conjugate gradient (NCG) methods for shape optimization problems. We briefly introduce the as well corresponding theoretical background and their performance numerically. The obtained results confirm that NCG are efficient attractive solution algorithms

We propose and study kernel conjugate gradient methods (KCGM) with random projections for least-squares regression over a separable Hilbert space. Considering two types of generated by randomized sketches Nyström subsampling, we prove optimal statistical results respect to variants norms the algorithms under suitable stopping rule. Particularly, our show that if projection dimension is proporti...

The conjugate gradient optimization algorithm usually used for nonlinear least squares is presented and is combined with the modified back propagation algorithm yielding a new fast training multilayer perceptron (MLP) algorithm (CGFR/AG). The approaches presented in the paper consist of three steps: (1) Modification on standard back propagation algorithm by introducing gain variation term of th...

Conjugate gradient methods have many advantages in real numerical experiments, such as fast convergence and low memory requirements. This paper considers a class of conjugate gradient learning methods for backpropagation (BP) neural networks with three layers. We propose a new learning algorithm for almost cyclic BP neural networks based on PRP conjugate gradient method. We then establish the d...