Michael W. Leonard

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Limited-memory BFGS quasi-Newton methods approximate the Hessian matrix of second derivatives by the sum of a diagonal matrix and a fixed number of rank-one matrices. These methods are particularly effective for large problems in which the approximate Hessian cannot be stored explicitly. It can be shown that the conventional BFGS method accumulates(More)
Quasi-Newton methods are reliable and eecient on a wide range of problems, but they can require many iterations if no good estimate of the Hessian is available or the problem is ill-conditioned. Methods that are less susceptible to ill-conditioning can be formulated by exploiting the fact that quasi-Newton methods accumulate second-derivative information in(More)
We propose a sequential quadratic programming (SQP) method for the optimal control of large-scale dynamical systems. The method uses modified multiple shooting to discretize the dynamical constraints. When these systems have relatively few parameters, the computational complexity of the modified method is much less than that of standard multiple shooting.(More)
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