We present and analyze a new damping approach called backward step control for the globalization of the convergence of Newton-type methods for the numerical solution of nonlinear root-finding problems. We provide and discuss reasonable assumptions that imply convergence of backward step control on the basis of generalized Newton paths in conjunction with a backward analysis argument. In particu...

This paper considers the connection between the intrinsic Riemannian Newton method and other more classically inspired optimization algorithms for equality-constrained optimization problems. We consider the feasibly-projected sequential quadratic programming (FP-SQP) method and show that it yields the same update step as the Riemannian Newton, subject to a minor assumption on the choice of mult...

Abstract In this paper, we suggest a new infeasible interior-point method (IIPM) for $$P_{*}(\kappa )$$ P ∗ ( κ ) -linear complementarity problem ( -LCP) based on class of kernel func...

In this paper, we propose a feasible primal-dual path-following algorithm for convex quadratic programs.At each interior-point iteration the algorithm uses a full-Newton step and a suitable proximity measure for tracing approximately the central path.We show that the short-step algorithm has the best known iteration bound,namely O( √ n log (n+1) ).

we present a modified version of the infeasible-interior- we present a modified version of the infeasible-interior-point algorithm for monotone linear complementary problems introduced by mansouri et al. (nonlinear anal. real world appl. 12(2011) 545--561). each main step of the algorithm consists of a feasibility step and several centering steps. we use a different feasibility step, which targ...

We present sufficient convergence conditions for two-step Newton methods in order to approximate a locally unique solution of a nonlinear equation in a Banach space setting. The advantages of our approach under the same computational cost over other studies such as [9–25] for the semilocal convergence case are: weaker sufficient convergence conditions, more precise error bounds on the distances...