This technical report is a companion to [5] that proves the diagonal blocks of the Hessian matrix for the inverse mean-ratio metric for tetrahedral elements are positive definite. Thus, the block Jacobi preconditioner used in the inexact Newton method to solve the mesh shape-quality optimization problem using the average inverse mean-ratio metric for the objective function is positive definite....

In a previous work the authors proved under a complex assumption on the set-valued mapping, the existence of Lipschitz solutions for second order convex sweeping processes in p-uniformly smooth and q-uniformly convex Banach spaces. In the present work we prove the same result, under a condition on the distance function to the images of the set-valued mapping. Our assumption is much simpler than...

The concept of uniform convexity of a Banach space was generalized to linear operators between Banach spaces and studied by Beauzamy [1]. Under this generalization, a Banach space X is uniformly convex if and only if its identity map IX is. Pisier showed that uniformly convex Banach spaces have martingale type p for some p > 1. We show that this fact is in general not true for linear operators....

We construct a new iterative scheme by hybrid methods and prove strong convergence theorem for approximation of a common fixed point of two countable families of closed relatively quasinonexpansive mappings which is also a solution to a system of equilibrium problems in a uniformly smooth and strictly convex real Banach space with Kadec-Klee property using the properties of generalized f -proje...

We consider a class of inverse problems defined by a nonlinear map from parameter or model functions to the data. We assume that solutions exist. The space of model functions is a Banach space which is smooth and uniformly convex; however, the data space can be an arbitrary Banach space. We study sequences of parameter functions generated by a nonlinear Landweber iteration and conditions under ...

Conjugate gradient methods are important for large-scale unconstrained optimization. This paper proposes an acceleration of these methods using a modification of steplength. The idea is to modify in a multiplicative manner the steplength k α , computed by Wolfe line search conditions, by means of a positive parameter k η , in such a way to improve the behavior of the classical conjugate gradien...

using a new set of ideas that combines dynamical systems techniques with control theory and viscosity solutions methods. In (1), H(p, x) : R → R is a smooth Hamiltonian, strictly convex, i.e., D vvL(x, v) > γ > 0 uniformly (this is also called uniformly convex by some authors), and coercive in p (lim|p|→∞ H(p,x) |p| = ∞), and Z n periodic in x (H(p, x + k) = H(p, x) for k ∈ Z). Since R is the u...