%-------------------------------------------------------------------------------
% UF Sparse Matrix Collection, Tim Davis
% http://www.cise.ufl.edu/research/sparse/matrices/VDOL/orbitRaising_3
% name: VDOL/orbitRaising_3
% [orbitRaising optimal control problem (matrix 3 of 4)]
% id: 2720
% date: 2015
% author: B. Senses, A. Rao
% ed: T. Davis
% fields: name title A b id date author ed kind notes aux
% aux: rowname mapping
% kind: optimal control problem
%-------------------------------------------------------------------------------
% 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}                                                
% }                                                                      
%-------------------------------------------------------------------------------
