Projected gradient iteration for nonlinear operator equation

Projected Power Iteration for Network Alignment

The network alignment problem asks for the best correspondence between two given graphs, so that the largest possible number of edges are matched. This problem appears in many scientific problems (like the study of protein-protein interactions) and it is very closely related to the quadratic assignment problem which has graph isomorphism, traveling salesman and minimum bisection problems as par...

A generalized conditional gradient method for nonlinear operator equations

The intention of this paper is to show the applicability of a generalized conditional gradient method for the minimization of Tikhonov-type functionals, which occur in the regularization of nonlinear inverse problems with sparsity constraints. We consider functionals of Tikhonov type where the usual quadratic penalty term is replaced by the pth power of a weighted p-norm. First of all, we analy...

The variational iteration method for solving Nagumo telegraph equation

Spectral Projected Gradient Methods

The poor practical behavior of (1)-(2) has been known for many years. If the level sets of f resemble long valleys, the sequence {xk} displays a typical zig-zagging trajectory and the speed of convergence is very slow. In the simplest case, in which f is a strictly convex quadratic, the method converges to the solution with a Q-linear rate of convergence whose factor tends to 1 when the conditi...

Gradient estimates for a nonlinear parabolic equation under Ricci flow

Let (M,g(t)), 0 ≤ t ≤ T , be a n-dimensional complete noncompact manifold, n ≥ 2, with bounded curvatures and metric g(t) evolving by the Ricci flow ∂gij ∂t = −2Rij . We will extend the result of L. Ma and Y. Yang and prove a local gradient estimate for positive solutions of the nonlinear parabolic equation ∂u ∂t = ∆u − au log u − qu where a ∈ R is a constant and q is a smooth function on M × [...