We consider the unconstrained minimization of a continuously diierentiable function with semismooth gradient by line search methods; in particular we focus on the problem of the acceptance of the unit stepsize. We show that, under mild conditions, if the full search direction brings superlinear convergence, then the unit stepsize is eventually accepted so that the Maratos eeect does not occur. ...

Some previous works show that symmetric fixedand variablestepsize linear multistep methods for second-order systems which do not have any parasitic root in their first characteristic polynomial give rise to a slow error growth with time when integrating reversible systems. In this paper, we give a technique to construct variable-stepsize symmetric methods from their fixed-stepsize counterparts,...

In this paper, we investigate a distributed Nash equilibrium seeking problem for a timevarying multi-agent network consisting of two subnetworks. We propose a subgradientbased distributed algorithm to seek a Nash equilibrium of a zero-sum game, where the two subnetworks share the same sum objective function. We show that the proposed distributed algorithm with homogenous stepsize can achieve a ...

The present work is concerned with the efficient time integration of nonlinear evolution equations by exponential operator splitting methods. Defect-based local error estimators serving as a reliable basis for adaptive stepsize control are constructed and analyzed. In the context of time-dependent nonlinear Schrödinger equations, asymptotical correctness of the local error estimators associated...

A fundamental classification problem of data mining and machine learning is that of minimizing a strongly convex, piecewise quadratic function on the n-dimensional real space Rn. We show finite termination of a Newton method to the unique global solution starting from any point in Rn. If the function is well conditioned, then no stepsize is required from the start, and if not, an Armijo stepsiz...

Volterra integro-differential equations with time-dependent delay arguments (DVIDEs) can provide us with realistic models of many real-world phenomena. Delayed LoktaVolterra predator-prey systems arise in Ecology and are well-known examples of DVIDEs first introduced by Volterra in 1928. We investigate the numerical solution of systems of DVIDEs using an adaptive stepsize selection strategy. We...

This paper presents adaptive algorithms for eigenvalue problems associated with non-selfadjoint partial differential operators. The basis for the developed algorithms is a homotopy method which departs from a wellunderstood selfadjoint problem. Apart from the adaptive grid refinement, the progress of the homotopy as well as the solution of the iterative method are adapted to balance the contrib...

We present a new algorithm for nonnegative least-squares (NNLS). Our algorithm extends the unconstrained quadratic optimization algorithm of Barzilai and Borwein (BB) (J. Barzilai and J. M. Borwein; Two-Point Step Size Gradient Methods. IMA J. Numerical Analysis; 1988.) to handle nonnegativity constraints. Our extension differs in several basic aspects from other constrained BB variants. The mo...

Energy-Based Error Control Strategies Suitable for Long MD Simulations Kante Easley Master of Science Graduate Department of Computer Science University of Toronto 2009 When evaluating integration schemes used in molecular dynamics (MD) simulations, energy conservation is often cited as the primary criterion by which the integrators should be compared. As a result variable stepsize Runge-Kutta ...

In this paper, we discuss an exponential integrator scheme, based on spatial discretization and time discretization, for a class of stochastic partial differential equations. We show that the scheme has a unique stationary distribution whenever the stepsize is sufficiently small, and that the weak limit of the stationary distribution of the scheme as the stepsize tends to zero is in fact the st...