11. Sequential methods

Sequential Methods and Their Applications

Sequential second derivative general linear methods for stiff systems

‎Second derivative general linear methods (SGLMs) as an extension‎ ‎of general linear methods (GLMs) have been introduced to improve‎ ‎the stability and accuracy properties of GLMs‎. ‎The coefficients of‎ ‎SGLMs are given by six matrices‎, ‎instead of four matrices for‎ ‎GLMs‎, ‎which are obtained by solving nonlinear systems of order and‎ ‎usually Runge--Kutta stability conditions‎. ‎In this p...

Computational Methods 11 - 04 and 11 Yxx

Future - Sequential Regularization Methods

We develop a theoretical context in which to study the future-sequential regularization method developed by J. V. Beck for the Inverse Heat Conduction Problem. In the process, we generalize Beck's ideas and view that method as one in a large class of regularization methods in which the solution of an ill-posed rst-kind Volterra equation is seen to be the limit of a sequence of solutions of well...

Sequential Quadratic Programming Methods ∗

In his 1963 PhD thesis, Wilson proposed the first sequential quadratic programming (SQP) method for the solution of constrained nonlinear optimization problems. In the intervening 48 years, SQP methods have evolved into a powerful and effective class of methods for a wide range of optimization problems. We review some of the most prominent developments in SQP methods since 1963 and discuss the ...