Parameter identification for an abstract Cauchy problem by quasilinearization
Abstract : A parameter identification problem is considered in the context of a linear abstract Cauchy problem with a parameter-dependent evolution operator. Conditions are investigated under which the gradient of the state with respect to a parameter possesses smoothness properties which lead to local convergence of an estimation algorithm based on quasilinearization. Numerical results are presented concerning estimation of unknown parameters in delay-differential equations. (JHD)
Convergence Rates of Quasi-Newton Algorithms for Some Nonsmooth Optimization Problems
In this paper we consider a class of nonsmooth optimization problems and investigate an algorithm which makes use of approximations of the derivative. We study a growth condition on the objective and various conditions on the step-sizes and the quasi-Newton operators to obtain linear, superlinear and quadratic rates of convergence. These results are applied to a class of Broyden updates and two inexact step-size rules.
Approximation schemes for nonlinear neutral optimal control systems
Abstract We discuss methods of approximating stable neutral functional differential equations and associated optimal control problems by sequences of optimal control problems for ordinary differential equations. By introducing a class of “mollified” neutral functional differential equations, convergence of the linear interpolating spline and the averaging approximation scheme is proved. A number of numerical examples are included.