We present the numerical solutions for the PDE-constrained optimization problem arising in cardiac electrophysiology, that is, the optimal control problem of monodomain model. The optimal control problem of monodomain model is a nonlinear optimization problem that is constrained by the monodomain model. The monodomain model consists of a parabolic partial differential equation coupled to a syst...

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...

The Steepest descent method and the Conjugate gradient to minimize nonlinear functions have been studied in this work. Algorithms are presented implemented Matlab software for both methods. However, a comparison has made between method. obtained results time efficiency aspects. It is shown that needs fewer iterations more than On other hand, converges function less

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In this report, several modifications of the nonlinear conjugate gradient method are described and investigated. Theoretical properties of these modifications are proved and their practical performance is demonstrated using extensive numerical experiments.

We combine linear algebra techniques with finite element techniques to obtain a reliable stopping cri-terion for Krylov method based algorithms. The Conjugate Gradient method has for a long time beensuccessfully used in the solution of the symmetric and positive definite systems obtained from thefinite-element approximation of self-adjoint elliptic partial differential equations...

In tensor completion, the goal is to fill in missing entries of a partially known tensor under a low-rank constraint. We propose a new algorithm that performs Riemannian optimization techniques on the manifold of tensors of fixed multilinear rank. More specifically, a variant of the nonlinear conjugate gradient method is developed. Paying particular attention to the efficient implementation, ou...

SUMMARY Existing multigrid techniques are used to eeect an eecient method for reconstructing an image from noisy, blurred data. Total Variation minimization yields a nonlinear integro-diierential equation which, when discretized using cell-centered-nite diierences, yields a full matrix equation. A xed point iteration is applied with the intermediate matrix equations solved via a preconditioned ...

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...