Direct and indirect methods for trajectory optimization
Annals of Operations Research - Special issue on nonlinear methods in economic dynamics and optimal control: Gmo¨or-series No. 2
Algorithm 755: ADOL-C: a package for the automatic differentiation of algorithms written in C/C++
ACM Transactions on Mathematical Software (TOMS)
Existence and multiple solutions of the minimum-fuel orbit transfer problem
Journal of Optimization Theory and Applications
Evaluating derivatives: principles and techniques of algorithmic differentiation
Evaluating derivatives: principles and techniques of algorithmic differentiation
Numerical Differentiation of Analytic Functions
ACM Transactions on Mathematical Software (TOMS)
Computation of sensitivity derivatives of Navier-Stokes equations using complex variables
Advances in Engineering Software - Special issue on large-scale analysis, design and intelligent synthesis environments
Accurate numerical derivatives in MATLAB
ACM Transactions on Mathematical Software (TOMS)
ADIFOR-Generating Derivative Codes from Fortran Programs
Scientific Programming
Fast higher-order derivative tensors with Rapsodia
Optimization Methods & Software
An efficient overloaded method for computing derivatives of mathematical functions in MATLAB
ACM Transactions on Mathematical Software (TOMS)
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The computations of the high-order partial derivatives in a given problem are often cumbersome or not accurate. To combat such shortcomings, a new method for calculating exact high-order sensitivities using multicomplex numbers is presented. Inspired by the recent complex step method that is only valid for firstorder sensitivities, the new multicomplex approach is valid to arbitrary order. The mathematical theory behind this approach is revealed, and an efficient procedure for the automatic implementation of the method is described. Several applications are presented to validate and demonstrate the accuracy and efficiency of the algorithm. The results are compared to conventional approaches such as finite differencing, the complex step method, and two separate automatic differentiation tools. The multicomplex method performs favorably in the preliminary comparisons and is therefore expected to be useful for a variety of algorithms that exploit higher order derivatives.