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/*-------------------------------------------------------------------------------
Copyright (c) 2014,2015 F. Georget <fabieng@princeton.edu>, Princeton University
All rights reserved.
Redistribution and use in source and binary forms, with or without modification,
are permitted provided that the following conditions are met:
1. Redistributions of source code must retain the above copyright notice, this
list of conditions and the following disclaimer.
2. Redistributions in binary form must reproduce the above copyright notice,
this list of conditions and the following disclaimer in the documentation and/or
other materials provided with the distribution.
3. Neither the name of the copyright holder nor the names of its contributors
may be used to endorse or promote products derived from this software without
specific prior written permission.
THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND
ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE FOR
ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
(INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON
ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
(INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
-----------------------------------------------------------------------------*/
#include "micpsolverold.hpp" // for syntaxic coloration...
#include "estimate_cond_number.hpp"
#include "utils/log.hpp"
#include <iostream>
//! \file micpsolver.inl implementation of the MiCP solver
namespace specmicp {
namespace micpsolver {
// Main algorithm
// ##############
template <class Program, NCPfunction ncp_t>
MiCPSolverReturnCode MiCPSolverOLD<Program, ncp_t>::solve(Eigen::VectorXd &x)
{
int cnt = 0;
if (get_options().use_crashing) crashing(x);
else setup_residuals(x);
MiCPSolverReturnCode retcode = MiCPSolverReturnCode::NotConvergedYet;
Eigen::VectorXd update(get_neq());
while (retcode == MiCPSolverReturnCode::NotConvergedYet)
{
DEBUG << "Iteration : " << cnt;
SPAM << "Solution : \n" << x;
m_program->hook_start_iteration(x, m_phi_residuals.norm());
setup_residuals(x);
get_perf().current_residual = m_phi_residuals.norm();
SPAM << "Residuals : \n ----- \n" << m_phi_residuals << "\n ----- \n";
retcode = check_convergence(cnt, update, x);
get_perf().return_code = retcode;
if (retcode != MiCPSolverReturnCode::NotConvergedYet) break;
++cnt;
m_max_taken = false;
setup_jacobian(x);
if(get_options().use_scaling)
search_direction_calculation(update);
else
search_direction_calculation_no_scaling(update);
reformulate_result<ncp_t>(get_neq(), get_neq_free(),
x, m_residuals,
m_grad_phi, update);
int termcode = linesearch(update, x);
get_perf().current_update = update.norm();
DEBUG << "Return LineSearch : " << termcode;
projection(x);
get_perf().nb_iterations = cnt;
}
return retcode;
}
template <class Program, NCPfunction ncp_t>
MiCPSolverReturnCode MiCPSolverOLD<Program, ncp_t>::check_convergence(int nb_iterations,
Eigen::VectorXd& update,
Eigen::VectorXd& solution)
{
MiCPSolverReturnCode termcode = MiCPSolverReturnCode::NotConvergedYet;
const double norm_residuals = m_phi_residuals.lpNorm<Eigen::Infinity>();
if (norm_residuals < get_options().fvectol)
{
termcode = MiCPSolverReturnCode::ResidualMinimized;
}
else if (nb_iterations >0 and norm_update<Eigen::Infinity>(update, solution) < get_options().steptol)
{
if (norm_residuals > get_options().threshold_stationary_point)
{
ERROR << "Stationary point detected !";
termcode = MiCPSolverReturnCode::StationaryPoint;
}
WARNING << "Error is minimized - may indicate a stationnary point";
termcode = MiCPSolverReturnCode::ErrorMinimized;
}
else if (nb_iterations > get_options().max_iter)
{
ERROR << "Maximum number of iteration reached (" << get_options().max_iter << ")";
termcode = MiCPSolverReturnCode::MaxIterations;
}
else if (m_max_taken)
{
++m_consec_max;
if (m_consec_max == get_options().maxiter_maxstep) {
ERROR << "Divergence detected - Maximum step length taken two many times";
termcode = MiCPSolverReturnCode::MaxStepTakenTooManyTimes;
}
}
else
{
m_consec_max = 0;
}
return termcode;
}
template <class Program, NCPfunction ncp_t>
MiCPSolverReturnCode MiCPSolverOLD<Program, ncp_t>::search_direction_calculation(Eigen::VectorXd& update)
{
Eigen::VectorXd rscaler(Eigen::VectorXd::Ones(m_jacobian.cols()));
Eigen::VectorXd cscaler(Eigen::VectorXd::Ones(m_jacobian.rows()));
scaling_jacobian(m_jacobian, m_phi_residuals, rscaler, cscaler);
m_jacobian = rscaler.asDiagonal() * (m_jacobian) * cscaler.asDiagonal();
Eigen::ColPivHouseholderQR<Eigen::MatrixXd> solver;
m_gradient_step_taken = false;
int m;
for (m=0; m<get_options().max_factorization_step; ++m)
{
const double lambda = get_options().factor_gradient_search_direction;
solver.compute(m_jacobian);
get_perf().nb_factorization += 1;
if (solver.info() != Eigen::Success or not solver.isInvertible())
{
DEBUG << "Solver.info : " << solver.info() << " - is invertible : " << solver.isInvertible();
ERROR << "System cannot be solved, we try a perturbation";
m_gradient_step_taken = true;
m_jacobian += rscaler.asDiagonal() * (
lambda*Eigen::MatrixXd::Identity(m_jacobian.rows(),m_jacobian.cols())) * cscaler.asDiagonal();
continue;
}
double cond = estimate_condition_number(solver.matrixR().triangularView<Eigen::Upper>());
if (cond > get_options().condition_limit)
{
m_gradient_step_taken = true;
m_jacobian += rscaler.asDiagonal() * (
lambda*Eigen::MatrixXd::Identity(m_jacobian.rows(),m_jacobian.cols())) * cscaler.asDiagonal();
continue;
}
update = solver.solve(-rscaler.cwiseProduct(m_phi_residuals + m*lambda*m_grad_phi));
update = cscaler.cwiseProduct(update);
double descent_cond = m_grad_phi.dot(update);
double norm_grad = m_grad_phi.norm();
double norm_update = update.norm();
if ( (descent_cond <= -get_options().factor_descent_condition*std::min(std::pow(norm_update,2),std::pow(norm_update,3)))
and (descent_cond <= -get_options().factor_descent_condition*std::min(std::pow(norm_grad,2),std::pow(norm_grad,3)))
)
break; // we have a solution !
m_gradient_step_taken = true;
m_jacobian += rscaler.asDiagonal() * ( lambda*
Eigen::MatrixXd::Identity(m_jacobian.rows(),m_jacobian.cols())
) * cscaler.asDiagonal();
}
DEBUG << "Gradient step : m = " << m;
if (m == get_options().max_factorization_step) {
INFO << "Full gradient step taken !";
update = -m_grad_phi;
}
return MiCPSolverReturnCode::NotConvergedYet;
}
template <class Program, NCPfunction ncp_t>
MiCPSolverReturnCode MiCPSolverOLD<Program, ncp_t>::search_direction_calculation_no_scaling(Eigen::VectorXd& update)
{
DEBUG << "Solving linear system";
Eigen::ColPivHouseholderQR<Eigen::MatrixXd> solver;
m_gradient_step_taken = false;
int m;
for (m=0; m<get_options().max_factorization_step; ++m)
{
const double lambda = get_options().factor_gradient_search_direction;
solver.compute(m_jacobian);
get_perf().nb_factorization += 1;
if (solver.info() != Eigen::Success or not solver.isInvertible()) continue;
double cond = estimate_condition_number(solver.matrixR().triangularView<Eigen::Upper>());
if (cond > get_options().condition_limit)
{
continue;
}
update = solver.solve(-(m_phi_residuals + m*lambda*m_grad_phi));
double descent_cond = m_grad_phi.dot(update);
double norm_grad = m_grad_phi.norm();
double norm_update = update.norm();
if ( (descent_cond <= -get_options().factor_descent_condition*std::min(std::pow(norm_update,2),std::pow(norm_update,3)))
and (descent_cond <= -get_options().factor_descent_condition*std::min(std::pow(norm_grad,2),std::pow(norm_grad,3)))
)
break; // we have a solution !
m_gradient_step_taken = true;
m_jacobian += lambda*Eigen::MatrixXd::Identity(m_jacobian.rows(),m_jacobian.cols());
}
DEBUG << "Gradient step : m = " << m;
if (m ==4) {
INFO << "Full gradient step taken !";
update = -m_grad_phi;
}
return MiCPSolverReturnCode::NotConvergedYet;
}
template <class Program, NCPfunction ncp_t>
void MiCPSolverOLD<Program, ncp_t>::crashing(Eigen::VectorXd &x)
{
DEBUG << "Crashing ";
const double beta = 0.5;
const double sigma = 1e-5;
int cnt = 0;
while (cnt < 10)
{
setup_residuals(x);
setup_jacobian(x);
m_grad_phi = m_jacobian.transpose()*m_phi_residuals;
Eigen::VectorXd xp(get_neq());
int l=0;
const int maxl = 10;
while (l<maxl)
{
xp = x - std::pow(beta, l)*m_grad_phi;
for (int i=get_neq_free(); i<get_neq(); ++i)
{
if (xp(i) < 0) xp(i) = 0;
}
Eigen::VectorXd new_res(get_neq());
compute_residuals(x, new_res);
reformulate_residuals_inplace(x, new_res);
double test = 0.5*(new_res.squaredNorm() - m_phi_residuals.squaredNorm()) + sigma*m_grad_phi.dot(x - xp);
if (test <= 0) break;
++l;
}
if (l == maxl) break;
x = xp;
++cnt;
}
get_perf().nb_crashing_iterations = cnt;
DEBUG << "Crashing iterations : " << cnt;
m_max_merits.reserve(4);
SPAM << "Solution after crashing \n ------ \n " << x << "\n ----- \n";
}
// Others
// ######
template <class Program, NCPfunction ncp_t>
void MiCPSolverOLD<Program, ncp_t>::reformulate_residuals(const Eigen::VectorXd& x,
const Eigen::VectorXd& r,
Eigen::VectorXd& r_phi)
{
r_phi.resizeLike(r);
r_phi.block(0, 0, get_neq_free(), 1) = r.block(0, 0, get_neq_free(), 1);
for (int i = get_neq_free(); i<get_neq(); ++i)
{
r_phi(i) = phi_lower_bounded(x(i), r(i), 0);
}
}
template <class Program, NCPfunction ncp_t>
void MiCPSolverOLD<Program, ncp_t>::reformulate_residuals_inplace(const Eigen::VectorXd& x,
Eigen::VectorXd& r)
{
for (int i = get_neq_free(); i<get_neq(); ++i)
{
r(i) = phi_lower_bounded(x(i), r(i), 0);
}
}
// ref : Munson et al. (2001)
template <class Program, NCPfunction ncp_t>
void MiCPSolverOLD<Program, ncp_t>:: scaling_jacobian(
const Eigen::MatrixXd& jacobian,
const Eigen::VectorXd& r_phi,
Eigen::VectorXd& rscaler,
Eigen::VectorXd& cscaler)
{
for (int i=0; i<jacobian.cols(); ++i)
{
const double sumhsq = jacobian.row(i).array().square().sum();
double s = std::sqrt(r_phi(i)*r_phi(i) + sumhsq);
rscaler(i) = 1.0/std::max(s, 1e-10);
}
for (int i=0; i<jacobian.cols(); ++i)
{
const double sumhsq = (rscaler.asDiagonal()*jacobian).col(i).array().square().sum();
double s = std::sqrt(sumhsq);
cscaler(i) = 1.0/std::max(s, 1e-10);
}
}
template <class Program, NCPfunction ncp_t>
int MiCPSolverOLD<Program, ncp_t>::linesearch(Eigen::VectorXd& p, Eigen::VectorXd& x)
{
// Reference Algo A6.3.1 : Dennis and Schnabel (1983)
DEBUG << "Linesearch";
Eigen::VectorXd xp(get_neq());
Eigen::VectorXd new_res(get_neq());
double fcp;
m_max_taken = false;
int retcode = 2;
const double alpha = 1e-6;
double newtlen = is_step_too_long(p);
double init_slope = m_grad_phi.dot(p);
double rellength = std::abs(p(0));
for (int i=1; i<get_neq(); ++i)
{
rellength = std::max(rellength, std::abs(p(i)));
}
double minlambda = get_options().steptol / rellength;
double lambda = m_program->max_lambda(x, p);
double lambda_prev = lambda;
// non monotone linesearch
// -----------------------
double merit_value = 0.5*m_phi_residuals.squaredNorm();
// new residual
xp = x + lambda*p;
compute_residuals(xp, new_res);
reformulate_residuals_inplace(xp, new_res);
fcp = 0.5*new_res.squaredNorm();
// Skip linesearch if enough progress is done
if (fcp < get_options().coeff_accept_newton_step *merit_value)
{
if (m_max_merits.size() > 0) m_max_merits[m_max_merits.size()-1] = merit_value;
else m_max_merits.push_back(merit_value);
x = xp;
return 0;
}
//std::cout << "Merit value : " << merit_value << std::endl;
double mmax = merit_value;
if (m_max_merits.size() > 0)
{
mmax = m_max_merits[m_max_merits.size()-1];
}
if (m_max_merits.size() < 4)
{
m_max_merits.push_back(merit_value);
if (merit_value < mmax) merit_value = (3*merit_value + mmax)/4;
}
else if (merit_value < mmax)
{
m_max_merits[3] = merit_value;
merit_value = mmax;
}
if (m_gradient_step_taken)
{
merit_value *= 100;
}
//std::cout << "Merit value used : " << merit_value << std::endl;
double fc = merit_value;
double fcp_prev;
int cnt = 0;
do
{
fcp = 0.5*new_res.squaredNorm();
//std::cout << "fcp : " << fcp << "\n fc+alin : " << fc+alpha*lambda*init_slope << " # fc : " << fc << std::endl;
if (fcp <= fc - std::min(-alpha*lambda*init_slope,(1-alpha)*fc)) //pg760 Fachinei2003
{
retcode = 0;
if (lambda ==1 and (newtlen > 0.99 * get_options().maxstep)) {
m_max_taken = true;
}
break;
}
else if (lambda < minlambda)
{
retcode = 1;
break;
}
else
{
double lambdatmp;
if (cnt == 0) { // only a quadratic at the first
lambdatmp = - init_slope / (2*(fcp - fc -init_slope));
}
else
{
const double factor = 1 /(lambda - lambda_prev);
const double x1 = fcp - fc - lambda*init_slope;
const double x2 = fcp_prev - fc - lambda_prev*init_slope;
const double a = factor * ( x1/(lambda*lambda) - x2/(lambda_prev*lambda_prev));
const double b = factor * ( -x1*lambda_prev/(lambda*lambda) + x2*lambda/(lambda_prev*lambda_prev));
if (a == 0)
{ // cubic interpolation is in fact a quadratic interpolation
lambdatmp = - init_slope/(2*b);
}
else
{
const double disc = b*b-3*a*init_slope;
lambdatmp = (-b+std::sqrt(disc))/(3*a);
}
if (lambdatmp > 0.5*lambda ) lambdatmp = 0.5*lambda;
}
lambda_prev = lambda;
fcp_prev = fcp;
if (lambdatmp < 0.1*lambda) {
lambda = 0.1 * lambda;
} else {
lambda = lambdatmp;
}
}
xp = x + lambda*p;
compute_residuals(xp, new_res);
reformulate_residuals_inplace(xp, new_res);
++cnt;
} while(retcode == 2 and cnt < 100);
DEBUG << "Lambda : " << lambda;
if (cnt == 100)
{
ERROR << "Too much linesearch iterations ! We stop";
}
x = xp;
p = lambda*p;
return retcode;
}
// Projection of the variables onto the feasible set
template <class Program, NCPfunction ncp_t>
void MiCPSolverOLD<Program, ncp_t>::projection(Eigen::VectorXd &x)
{
for (int i=0; i<m_program->nb_complementarity_variables(); ++i)
{
if (x(i+m_program->nb_free_variables()) < get_options().projection_min_variable)
{
x(i+m_program->nb_free_variables()) = 0;
}
}
}
template <class Program, NCPfunction ncp_t>
double MiCPSolverOLD<Program, ncp_t>::is_step_too_long(Eigen::VectorXd& update)
{
double steplength = update.norm();
if (steplength > get_options().maxstep)
{
m_max_taken = true;
update = get_options().maxstep / steplength * update;
steplength = get_options().maxstep;
}
return steplength;
}
// ================================================= //
// //
// NCP functions and reformulation //
// //
// ================================================= //
template <>
inline double ncp_function<NCPfunction::penalizedFB>(double a, double b, double t)
{
return penalized_fisher_burmeister(a, b, t);
}
template <>
inline double ncp_function<NCPfunction::min>(double a, double b, double _)
{
return std::min(a, b);
}
template <>
inline void reformulate_jacobian_helper<NCPfunction::penalizedFB>(
int neq,
int neq_free,
const Eigen::VectorXd& x,
const Eigen::VectorXd& r,
Eigen::MatrixXd& jacobian,
Eigen::VectorXd& _,
double t
)
{
// set the z vector : contains 1 for degenerate points
Eigen::VectorXd z(Eigen::VectorXd::Zero(neq));
for (int i=neq_free; i<neq; ++i)
{
if (x(i) == 0 and r(i) == 0)
z(i) = 1.0;
}
// modify the jacobian
const double lambda = t;
for (int i=neq_free; i<neq; ++i)
{
Eigen::VectorXd grad_fi = jacobian.block(i, 0, 1, neq).transpose();
if (z(i) != 0)
{
double gpdotz = grad_fi.dot(z);
double s = std::abs(z(i)) + std::abs(gpdotz);
s = s * std::sqrt(z(i)*z(i)/(s*s) + gpdotz*gpdotz/(s*s));
const double c = lambda*(z(i)/s - 1);
const double d = lambda*(gpdotz/s -1);
grad_fi = d*grad_fi;
grad_fi(i) += c;
}
else
{
double s = std::abs(x(i)) + std::abs(r(i));
s = s * std::sqrt(x(i)*x(i)/(s*s) + r(i)*r(i)/(s*s));
double c = lambda*(x(i)/s - 1);
double d = lambda*(r(i)/s - 1);
if ((lambda <1) and (r(i) > 0) and (x(i) >0))
{
c -= (1-lambda)*r(i);
d -= (1-lambda)*x(i);
}
grad_fi = d*grad_fi;
grad_fi(i) += c;
}
jacobian.block(i, 0, 1, neq) = grad_fi.transpose();
}
}
template <>
inline void reformulate_jacobian_helper<NCPfunction::min>(
int neq,
int neq_free,
const Eigen::VectorXd& x,
const Eigen::VectorXd& r,
Eigen::MatrixXd& jacobian,
Eigen::VectorXd& r_phi,
double _
)
{
std::vector<int> to_keep;
to_keep.reserve(10);
Eigen::VectorXd to_remove(neq-neq_free);
for (int i=neq_free; i<neq; ++i)
{
if (x(i) >= r(i))
{
to_remove(i-neq_free) = 0;
to_keep.push_back(i);
}
else
to_remove(i-neq_free) = x(i);
}
r_phi.block(0, 0, neq_free, 1) -= jacobian.block(0, neq_free, neq_free, neq-neq_free)*to_remove;
int new_i = neq_free;
for (auto it=to_keep.begin(); it!=to_keep.end(); ++it)
{
//r_phi.block(0, 0, neq_free, 1) += x(*it)*jacobian.block(0, *it, neq_free, 1);
jacobian.block(new_i, 0, 1, neq_free) = jacobian.block(*it, 0, 1, neq_free); // the bottom right corner is 0
jacobian.block(0, new_i, neq_free, 1) = jacobian.block(0, *it, neq_free, 1);
r_phi(new_i) = r_phi(*it);
++new_i;
}
r_phi.conservativeResize(new_i);
jacobian.conservativeResize(new_i, new_i);
DEBUG << jacobian;
}
template <>
inline void reformulate_result<NCPfunction::penalizedFB>(
int neq,
int neq_free,
Eigen::VectorXd& x,
const Eigen::VectorXd& orig_r,
Eigen::VectorXd& grad_phi,
Eigen::VectorXd& update
)
{}
template <>
inline void reformulate_result<NCPfunction::min>(
int neq,
int neq_free,
Eigen::VectorXd& x,
const Eigen::VectorXd& orig_r,
Eigen::VectorXd& grad_phi,
Eigen::VectorXd& update
)
{
//std::cout << " Update \n ------- \n " << update << std::endl;
int tot_to_keep = 0;
for (int i=neq_free; i<neq; ++i)
{
if (x(i) >= orig_r(i))
++tot_to_keep;
}
//std::cout << " update \n ------ \n" << update.block(neq_free, 0, tot_to_keep, 1) << std::endl;
update.conservativeResize(neq);
grad_phi.conservativeResize(neq);
int kept_i = 1;
for (int i=neq-1; i>=neq_free; --i)
{ // we go backwards to avoid extra copies
//std::cout << i << " # " << x(i) << " - " << orig_r(i) << std::endl;
if (x(i) >= orig_r(i))
{
//std::cout << i << std::endl;
update(i) = update(neq_free+(tot_to_keep-kept_i));
//std::cout << update(i) << std::endl;
grad_phi(i) = grad_phi(neq_free+(tot_to_keep-kept_i));
++kept_i;
}
else
{
//x(i) = 0.0;
//update(i) = 0.0;
update(i) = -x(i);
grad_phi(i) = x(i);
}
}
}
} // end namespace micpsolver
} // end namespace specmicp

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