Methods and software for derivative-based numerical optimization in general and simulation-based optimization in particular have seen a large rise in popularity over the past 30 years. Still, due to practical difficulties in implementing many of the methods in a fast and reliable manner, it remains an underused technology both in academia and in industry. To address this, we present a set of methods and tools with the aim of making techniques for dynamic optimization more accessible. In particular, we present CasADi, an open-source software framework for numerical optimization and algorithmic differentiation (AD) that offers a level of abstraction which is lower than algebraic modeling languages, but higher than conventional AD tools. We also discuss several of the many application problems which have already been addressed with CasADi by researchers from diverse fields.

https://lirias.kuleuven.be/bitstream/123456789/418048/1/thesis_final2.pdf

A General-Purpose Software Framework for Dynamic Optimization

Dispersion-managed solitons in fibre systems and lasers

A General-Purpose Software Framework for Dynamic Optimization (Een algemene softwareomgeving voor dynamische optimalisatie)

On shooting methods for boundary value problems

A robust Bézier based solution for nonlinear vibration and post-buckling of random checkerboard graphene nano-platelets reinforced composite beams

The common techniques for solving two-point boundary value problems can be classified as either "shooting" or "finite difference" methods. Central to a shooting method is the ability to integrate the differential equations as an initial value problem with guesses for the unknown initial values. This ability is not required with a finite difference method, for the unknowns are considered to be the values of the true solution at a number of interior mesh points. Each method has its advantages and disadvantages. One serious shortcoming of shooting becomes apparent when, as happens altogether too often, the differential equations are so unstable that they "blow up" before the initial value problem can be completely integrated. This can occur even in the face of extremely accurate guesses for the initial values. Hence, shooting seems to offer no hope for some problems. A finite difference method does have a chance for it tends to keep a firm hold on the entire solution at once. The purpose of this note is to point out a compromising procedure which endows shooting-type methods with this particular advantage of finite difference methods. For such problems, then, all hope need not be abandoned for shooting methods. This is desirable because shooting methods are generally faster than finite difference methods.The organization is as follows: I. The two-point boundary value problem is stated in quite general form. II. A particular shooting method is described which is designed to solve the problem in this form. III. The two-point boundary value problem is then restated in such a way that: (a) the restatement still falls within the general form, and (b) the shooting method now has a better chance of success when the equations are unstable.

/pdf/multiple-shooting-method-for-two-point-boundary-value-36zr7q7hrq.pdf

Multiple shooting method for two-point boundary value problems

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Multiple shooting method for two-point boundary value problems