/*
The quadprog_solve() function implements the algorithm of Goldfarb and Idnani
for the solution of a (convex) Quadratic Programming problem
by means of an active-set dual method.
The problem is in the form:
min 0.5 * x G x + g0 x
s.t.
CE^T x + ce0 = 0
CI^T x + ci0 >= 0
The matrix and vectors dimensions are as follows:
G: n * n
g0: n
CE: n * p
ce0: p
CI: n * m
ci0: m
x: n
The function will return the cost of the solution written in the x vector or
std::numeric_limits::infinity() if the problem is infeasible. In the latter case
the value of the x vector is not correct.
References: D. Goldfarb, A. Idnani. A numerically stable dual method for solving
strictly convex quadratic programs. Mathematical Programming 27 (1983) pp. 1-33.
Notes:
1. pay attention in setting up the vectors ce0 and ci0.
If the constraints of your problem are specified in the form
A^T x = b and C^T x >= d, then you should set ce0 = -b and ci0 = -d.
2. The matrix G is modified within the function since it is used to compute
the G = L^T L cholesky factorization for further computations inside the function.
If you need the original matrix G you should make a copy of it and pass the copy
to the function.
Author: Luca Di Gaspero
DIEGM - University of Udine, Italy
l.digaspero@uniud.it
http://www.diegm.uniud.it/digaspero/
The author will be grateful if the researchers using this software will
acknowledge the contribution of this function in their research papers.
LICENSE
This file is part of QuadProg++: a C++ library implementing
the algorithm of Goldfarb and Idnani for the solution of a (convex)
Quadratic Programming problem by means of an active-set dual method.
Copyright (C) 2007-2009 Luca Di Gaspero.
Copyright (C) 2009 Eric Moyer.
QuadProg++ is free software: you can redistribute it and/or modify
it under the terms of the GNU Lesser General Public License as published by
the Free Software Foundation, either version 3 of the License, or
(at your option) any later version.
QuadProg++ is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU Lesser General Public License for more details.
You should have received a copy of the GNU Lesser General Public License
along with QuadProg++. If not, see .
*/
#ifndef _QUADPROGPP
#define _QUADPROGPP
#include "vislearning/optimization/quadprog/Array.h"
namespace QuadProgPP{
double solve_quadprog(Matrix& G, Vector& g0,
const Matrix& CE, const Vector& ce0,
const Matrix& CI, const Vector& ci0,
Vector& x);
}
#endif // #define _QUADPROGPP