Gould and Robinson (NAR 08/18, Oxford University Computing Laboratory, 2008) gave global convergence results for a second-derivative SQP method for minimizing the exact l1-merit function for a fixed value of the penalty parameter. To establish this result, we used the properties of the so-called Cauchy step, which was itself computed from the so-called predictor step. In addition, we allowed fo...

Optimization plays a key role in machine learning. Recently, stochastic second-order methods have attracted much attention due to their low computational cost in each iteration. However, these algorithms might perform poorly especially if it is hard to approximate the Hessian well and efficiently. As far as we know, there is no effective way to handle this problem. In this paper, we resort to N...

IAPUNOV’S second method has long been recognized in the Soviet Union as the most general method for the study of the stability of equlibirum positions of systems described by differential or difference equations. The method was first presented by Liapunov in his now classical memoir,’ which appeared in Russian in 1892 and was translated into French in 1907. Good sources for the statements and p...

Converse Lyapunov theorems are presented for nonautonomous systems modelled as skew product flows. These characterize various types of stability of invariant sets and pullback, forward and uniform attractors in such nonautonomous systems. MSC subject classification: 37B25, 37B55, 93D30

The identiication of vector-valued FIR transfert functions using exclusively second-order statistics has become conventional. The so-called Subspace Method provides a nice and eecient way of solving the problem. However, the extension to the Multi-Input/Multi-Output (MIMO) case is not that straightforward and, for instance, some severe indetermination drawbacks may occur. We show in this paper ...

In [19], we gave global convergence results for a second-derivative SQP method for minimizing the exact l1-merit function for a fixed value of the penalty parameter. To establish this result, we used the properties of the so-called Cauchy step, which was itself computed from the so-called predictor step. In addition, we allowed for the computation of a variety of (optional) SQP steps that were ...

In this paper we describe a methodology for determining corrections to parameters and initial conditions in order to improve model forecasts in the presence of data. This methodology is grounded in the variational problem of minimizing the norm of the errors between forecast and data. The general method is presented, and then the method is applied to the specific example of a scalar model, the ...

Sequential quadratic programming (SQP) methods form a class of highly efficient algorithms for solving nonlinearly constrained optimization problems. Although second derivative information may often be calculated, there is little practical theory that justifies exact-Hessian SQP methods. In particular, the resulting quadratic programming (QP) subproblems are often nonconvex, and thus finding th...

Sequential quadratic programming (SQP) methods form a class of highly efficient algorithms for solving nonlinearly constrained optimization problems. Although second derivative information may often be calculated, there is little practical theory that justifies exact-Hessian SQP methods. In particular, the resulting quadratic programming (QP) subproblems are often nonconvex, and thus finding th...

Abstract : A selfstarting hybrid linear multistep method for direct solution of the general second-order initial value problem is considered. The continuous method is used to obtain Multiple Finite Difference Methods (MFDMs) (each of order 7) which are combined as simultaneous numerical integrators to provide a direct solution to IVPs over sub-intervals which do not overlap. The convergence of ...