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Fundamentals of Algorithms 7 This book gives an introduction to the practical treatment of inverse problems by means of numerical methods, with a focus on basic mathematical and computational aspects. It includes a number of tutorial exercises that give the reader hands-on experience. This introduction to computer-based problem-solving using the MATLAB ®… (More)

It has been observed that optimization codes are sometimes able to solve state constrained optimal control problems with discretizations which do not converge when used as an integrator on the constrained dynamics. Understanding this phenomenon could lead to a more robust design for direct transcription codes as well as better test problems. This paper… (More)

This second edition of the author's acclaimed textbook covers the major topics of computational linear algebra, including solution of a system of linear equations, least-squares solutions of linear systems, computation of eigenvalues, eigenvectors, and singular value problems. Important features of the original edition have been updated and improved. This… (More)

- John T. Betts, Stephen L. Campbell, Anna Engelsone
- 2004

— Direct transcription is a popular way to solve the complex optimal control problems that arise in industry. With a direct transcription approach, the problem is fully discretized and then the discrete problem is solved numerically. Recently it has been shown that the theory for direct transcription differs in several key ways from the theory for other… (More)

The numerical theory for Implicit Runge Kutta methods shows that there can be order reduction when these methods are applied to either stiff or differential algebraic equations. A previous paper introduced a way to try and compensate for this order reduction in designing mesh refinement strategies. This paper presents the results from a number of… (More)

Historically, researchers have solved optimal control problems using the calculus of variations-an approach called the indirect method. This technique led to the solution of a multipoint boundary value problem. Unfortunately, in practice, the indirect method is often insufficient. To eliminate the indirect method's deficiencies, an approach called direct… (More)

There have been a number of results in the literature showing that a direct transcription numerical approach to optimal control problems could have a number of surprising and desirable behaviors that were not always predicted by the existing theory especially when differential algebraic equations are involved. Most of these results were developed with an… (More)