This paper presents the hybrid algorithm of global optimization of dynamic learning rate for multilayer feedforward neural networks (MLFNN). The effect of inexact line search on conjugacy was studied and a generalized conjugate gradient method based on this effect was proposed and shown to have global convergence for error backpagation of MLFNN. The descent property and global convergence was g...

In this paper, we aim to solve an inverse robust optimization problem, in which the parameters in both the objective function and the robust constraint set need to be adjusted as little as possible so that a known feasible solution becomes the optimal one. We formulate this inverse problem as a minimization problem with a linear equality constraint, a second-order cone complementarity constrain...

In this article, a new inexact alternating direction method(ADM) is proposed for solving a class of variational inequality problems. At each iteration, the new method firstly solves the resulting subproblems of ADM approximately to generate an temporal point x̃, and then the multiplier y is updated to get the new iterate y. In order to get x, we adopt a new descent direction which is simple comp...

This paper studies convergence analysis of a preconditioned inexact Uzawa method for nondi erentiable saddle-point problems. The SOR-Newton method and the SOR-BFGS method are special cases of this method. We relax the Bramble– Pasciak–Vassilev condition on preconditioners for convergence of the inexact Uzawa method for linear saddle-point problems. The relaxed condition is used to determine the...

1:30 Inexact Solves in Interpolatory Model Reduction, SERKAN GUGERCIN, CHRISTOPHER BEATTIE, AND SARAH WYATT (Department of Mathematics). We expand upon the work of Beattie and Gugercin, who examined the role of inexact solves in the interpolation-based model reduction setting. We show the effect of inexact solves in one-sided and two-sided interpolation-based reduction as well as for the optima...

The R5RS specification of numerical operations leads to unportable and intransparent behavior of programs. Specifically, the notion of “exact/inexact numbers” and the misleading distinction between “real” and “rational” numbers are two primary sources of confusion. Consequently, the way R5RS organizes numbers is significantly less useful than it could be. Based on this diagnosis, we propose to ...

We propose a new technique for minimization of convex functions not necessarily smooth. Our approach employs an equivalent constrained optimization problem and approximated linear programs obtained with cutting planes. At each iteration a search direction and a step length are computed. If the step length is considered “non serious”, a cutting plane is added and a new search direction is comput...

For any continuous bilinear form defined on a pair of Hilbert spaces satisfying the compatibility Ladyshenskaya-Babušca-Brezzi condition, symmetric Schur complement operators can be defined on each of the two Hilbert spaces. In this paper, we find bounds for the spectrum of the Schur operators only in terms of the compatibility and continuity constants. In the light of the new spectral results ...

When a quantity is measured, the outcome depends on several factors like the measuring system, the measurement procedure, the skill of the operator, the environment, and other effects. In case of inexact quantity the outcome may also depends on the uncertainty representation. Recently inexact numbers got a lot of attention from many researchers in different fields. In this paper, we have tried ...

We study the local convergence of several inexact numerical algorithms closely related to Newton’s method for the solution of a simple eigenpair of the general nonlinear eigenvalue problem T (λ)v = 0. We investigate inverse iteration, Rayleigh quotient iteration, residual inverse iteration, and the single-vector Jacobi-Davidson method, analyzing the impact of the tolerances chosen for the appro...