%-------------------------------------------------------------------------------
% UF Sparse Matrix Collection, Tim Davis
% http://www.cise.ufl.edu/research/sparse/matrices/VDOL/goddardRocketProblem_2
% name: VDOL/goddardRocketProblem_2
% [goddardRocketProblem optimal control problem (matrix 2 of 2)]
% id: 2690
% 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/goddardRocketProblem                                              
%                                                                        
% Goddard rocket maximum ascent optimal control problem is taken from    
% Ref.~\cite{goddard1920method}. The goal of the Goddard rocket maximum  
% ascent problem is to determine the state and the control that          
% maximize the final altitude of an ascending rocket. The state of the   
% system is defined by the altitude, velocity, and the mass of the       
% rocket and the control of the system is the thrust. The Goddard        
% rocket problem contains a singular arc where the continuous-time       
% optimality conditions are indeterminate, thereby the nonlinear         
% programming problem solver will have difficulty determining the        
% optimal control during the singular arc. In order to prevent this      
% difficulty and obtain more accurate solutions the Goddard rocket       
% problem is posed as a three-phase optimal control problem. Phase one   
% and phase three contains the same dynamics and the path constraints    
% as the original problem, while phase two contains an additional path   
% constraint and an event constraint. The specified accuracy tolerance   
% of $10^{-8}$ were satisfied after two mesh iterations. As the mesh     
% refinement proceeds, the size of the KKT matrices increases from 831   
% to 867.                                                                
%                                                                        
% @article{goddard1920method,                                            
%   title={A Method of Reaching Extreme Altitudes.},                     
%   author={Goddard, Robert H},                                          
%   journal={Nature},                                                    
%   volume={105},                                                        
%   pages={809--811},                                                    
%   year={1920}                                                          
% }                                                                      
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