In this paper, a new kind of multigrid method is proposed for the ground state solution Bose–Einstein condensates based on Newton iteration scheme. Instead treating eigenvalue $$\lambda $$ and eigenvector u separately, we regard eigenpair $$(\lambda , u)$$ as one element in composite space $${\mathbb {R}} \times H_0^1(\varOmega )$$ then step adopted nonlinear problem. Thus scheme, main computat...

This paper proposes and analyzes a proximal augmented Lagrangian (NL-IAPIAL) method for solving constrained nonconvex composite optimization problems, where the constraints are smooth convex with respect to order given by closed cone. Each NL-IAPIAL iteration consists of inexactly subproblem an accelerated gradient followed Lagrange multiplier update. Under some mild assumptions, complexity bou...

A hierarchical version of the composite grid method (denoted as HFAC), which exploits the solution of the shell model in studying local effects via 3D solid model, is developed. Convergence studies on a beam/2D model problem indicate that the spectral radius of the point iteration matrix for the HFAC method is and with exact and approximate auxiliary coarse grid solutions, respectively, where L...

we present an improved version of a full nesterov-todd step infeasible interior-point method for linear complementarityproblem over symmetric cone (bull. iranian math. soc.,40(3), 541-564, (2014)). in the earlier version, each iteration consistedof one so-called feasibility step and a few -at most three -centering steps. here, each iteration consists of only a feasibilitystep. thus, the new alg...