In this work, we give a tight estimate of the rate of convergence for the Halpern-iteration for approximating a fixed point of a nonexpansive mapping in a Hilbert space. Specifically, using semidefinite programming and duality we prove that the norm of the residuals is upper bounded by the...

We study the almost periodic solutions of Euler equations and of some more general difference equations. We consider two different notions of almost periodic sequences, and we establish some relations between them. We build suitable sequences spaces and we prove some properties of these spaces....

<Para ID="Par1">We discuss a certain special subset of Lagrange multipliers, called critical, which usually exist when multipliers associated to a given solution are not unique. This kind of multipliers appear to be important for a number of reasons, some understood better, some (currently) not fully. What is...</para>

This paper establishes the superlinear convergence of a symmetric primal-dual path following algorithm for semidefinite programming under the assumptions that the semidefinite program has a strictly complementary primal-dual optimal solution and that the size of the central path neighborhood...

We present a local convergence analysis of the method of multipliers for equality-constrained variational problems (in the special case of optimization, also called the augmented Lagrangian method) under the sole assumption that the dual starting point is close to a noncritical Lagrange...

In this paper, we propose a new sequential systems of linear equations (SSLE) filter algorithm, which is an infeasible QP-free method. The new algorithm needs to solve a few reduced systems of linear equations with the same nonsingular coefficient matrix, and after finitely many iterations, only...

In many decision problems, criteria occur that can be expressed as ratios. The corresponding optimization problems are nonconvex programs of fractional type. In this paper, an algorithm for the numerical solution of these problems is introduced that converges always at superlinear speed....