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Unless Bosanac has a last minute change, the paper is done!

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Connor
2022-03-15 20:34:31 -06:00
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LaTeX/trajectory_optimization.tex
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The other category is the direct methods. In a direct optimization problem, the cost
function itself provides a value that an iterative numerical optimizer can measure
itself against. The optimal solution is then found by varying the inputs $x$ until the
itself against. The optimal solution is then found by varying the inputs $\vec{x}$ until the
cost function is reduced to a minimum value, often determined by its derivative
jacobian. A number of tools have been developed to optimize NLPs via this direct method
in the general case.
@@ -48,7 +48,7 @@
University. It uses a sparse sequential quadratic programming algorithm as its
back-end optimization scheme.
Another common NLP optimization packages (and the one used in this implementation)
Another common NLP optimization package (and the one used in this implementation)
is the Interior Point Optimizer or IPOPT\cite{wachter2006implementation}. It uses
an Interior Point Linesearch Filter Method and was developed as an open-source
project by the organization COIN-OR under the Eclipse Public License.
@@ -74,11 +74,6 @@
step the initial guess, now labeled $x_{k+1}$ after the addition of the ``step''
vector and iterates this process until predefined termination conditions are met.
In this case, the IPOPT algorithm was used, not as an optimizer, but as a solver. For
reasons that will be explained in the algorithm description in Section~\ref{algorithm} it
was sufficient merely that the non-linear constraints were met, therefore optimization (in
the particular step in which IPOPT was used) was unnecessary.
\subsubsection{Shooting Schemes for Solving a Two-Point Boundary Value Problem}
One straightforward approach to trajectory corrections is a single shooting
@@ -154,8 +149,7 @@
very well to low-thrust arcs and, in fact, Sims-Flanagan Transcribed low-thrust arcs
in particular, because there actually are control thrusts to be optimized at a
variety of different points along the orbit. This is, however, not an exhaustive
description of ways that multiple shooting can be used to optimize a trajectory,
simply the most convenient for low-thrust arcs.
description of ways that multiple shooting can be used to optimize a trajectory.
\section{Monotonic Basin Hopping Algorithms}