Self-concordant functions are a special class of convex functions in Euclidean space introduced by Nesterov. They are used in interior point methods, based on Newton iterations, where they play an important role in solving efficiently certain constrained optimization problems. The concept of self-concordant functions has been defined on Riemannian manifolds by Jiang et al. and a damped Newton m...

This paper presents a conjugate gradient-based algorithm for feedback min–max optimal control of nonlinear systems. The algorithm has a backward-in-time recurrent structure similar to the back propagation through time (BPTT) algorithm. The control law is given as the output of the one-layer NN. Main contribution of the paper includes the integration of BPTT techniques, conjugate gradient method...

Graphical processing units introduce the capability for large scale computation in the desk top environment. For the solution of linear systems of equations, much effort has been devoted to efficient implementation of Krylov subspace-based solvers in high performance computing environments. Here the focus is to improve the computational efficiency of the projected conjugate gradient algorithm. ...

Haemophilus influenzae, a major cause of meningitis in young children leading to death and other neurological sequelae. The disease leaves 15 to 35% of the survivors with permanent disabilities, such as, mental retardation or deafness. Despite the availability of new and more powerful antibiotics children with Hib meningitis still suffer from high mortality or morbidity. The emergence of multir...

We propose a novel variant of the conjugate gradient algorithm, Kernel Conjugate Gradient (KCG), designed to speed up learning for kernel machines with differentiable loss functions. This approach leads to a better conditioned optimization problem during learning. We establish an upper bound on the number of iterations for KCG that indicates it should require less than the square root of the nu...

Partial spectral information associated with the smallest eigenvalues can be used to improve the solution of successive linear systems of equations, namely in the simulation of time-dependent partial differential equations, where at each time step there are several systems with the same spectral properties to be solved. We propose to perform a partial spectral decomposition with the BlockCGSI a...