Matrix: VDOL/orbitRaising_4

Description: orbitRaising optimal control problem (matrix 4 of 4)

 (undirected graph drawing)

• Matrix group: VDOL
• download as a MATLAB mat-file, file size: 84 KB. Use UFget(2721) or UFget('VDOL/orbitRaising_4') in MATLAB.

 Matrix properties number of rows 915 number of columns 915 nonzeros 7,790 structural full rank? yes structural rank 915 # of blocks from dmperm 3 # strongly connected comp. 2 explicit zero entries 0 nonzero pattern symmetry symmetric numeric value symmetry symmetric type real structure symmetric Cholesky candidate? no positive definite? no

 author B. Senses, A. Rao editor T. Davis date 2015 kind optimal control problem 2D/3D problem? no

 Additional fields size and type b full 915-by-1 rowname full 915-by-79 mapping full 915-by-1

Notes:

```Optimal control problem, Vehicle Dynamics & Optimization Lab, UF
Anil Rao and Begum Senses, University of Florida
http://vdol.mae.ufl.edu

This matrix arises from an optimal control problem described below.
Each optimal control problem gives rise to a sequence of matrices of
different sizes when they are being solved inside GPOPS, an optimal
control solver created by Anil Rao, Begum Senses, and others at in VDOL
lab at the University of Florida.  This is one of the matrices in one
of these problems.  The matrix is symmetric indefinite.

Rao, Senses, and Davis have created a graph coarsening strategy
that matches pairs of nodes.  The mapping is given for this matrix,
where map(i)=k means that node i in the original graph is mapped to
node k in the smaller graph.  map(i)=map(j)=k means that both nodes
i and j are mapped to the same node k, and thus nodes i and j have
been merged.

This matrix consists of a set of nodes (rows/columns) and the
names of these rows/cols are given

Anil Rao, Begum Sense, and Tim Davis, 2015.

VDOL/orbitRaising

Orbit raising problem that is taken from
Ref.~\cite{bryson1975applied}. The goal of the optimal control
problem is to determine the state and the control that maximize the
radius of an orbit transfer in a given time. The state of the system
is defined by radial distance of the spacecraft from the attracting
center (e.g Earth, Mars, etc.) and velocity of the spacecraft and the
control is the thrust direction. The specified accuracy tolerance of
\$10^{-8}\$ were satisfied after four mesh iterations. As the mesh
refinement proceeds, the size of the KKT matrices increases from 442
to 915.

@book{bryson1975applied,
title={Applied Optimal Control: Optimization, Estimation, and
Control},
author={Bryson, Arthur Earl},
year={1975},
publisher={CRC Press}
}
```

 Ordering statistics: result nnz(chol(P*(A+A'+s*I)*P')) with AMD 9,543 Cholesky flop count 1.4e+05 nnz(L+U), no partial pivoting, with AMD 18,171 nnz(V) for QR, upper bound nnz(L) for LU, with COLAMD 13,957 nnz(R) for QR, upper bound nnz(U) for LU, with COLAMD 31,414