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solver.hpp
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// This file is part of PIQP.
//
// Copyright (c) 2024 EPFL
// Copyright (c) 2022 INRIA
//
// This source code is licensed under the BSD 2-Clause License found in the
// LICENSE file in the root directory of this source tree.
#ifndef PIQP_SOLVER_HPP
#define PIQP_SOLVER_HPP
#include <cstdio>
#include <Eigen/Dense>
#include <Eigen/Sparse>
#include "piqp/fwd.hpp"
#include "piqp/common.hpp"
#include "piqp/timer.hpp"
#include "piqp/results.hpp"
#include "piqp/settings.hpp"
#include "piqp/dense/data.hpp"
#include "piqp/dense/preconditioner.hpp"
#include "piqp/dense/kkt.hpp"
#include "piqp/sparse/data.hpp"
#include "piqp/sparse/preconditioner.hpp"
#include "piqp/sparse/kkt.hpp"
#include "piqp/utils/optional.hpp"
namespace piqp
{
enum SolverMatrixType
{
PIQP_DENSE = 0,
PIQP_SPARSE = 1
};
template<typename Derived, typename T, typename I, typename Preconditioner, int MatrixType, int Mode = KKTMode::KKT_FULL>
class SolverBase
{
protected:
using DataType = typename std::conditional<MatrixType == PIQP_DENSE, dense::Data<T>, sparse::Data<T, I>>::type;
using KKTType = typename std::conditional<MatrixType == PIQP_DENSE, dense::KKT<T>, sparse::KKT<T, I, Mode>>::type;
using CMatRefType = typename std::conditional<MatrixType == PIQP_DENSE, CMatRef<T>, CSparseMatRef<T, I>>::type;
Timer<T> m_timer;
Result<T> m_result;
Settings<T> m_settings;
DataType m_data;
Preconditioner m_preconditioner;
KKTType m_kkt;
bool m_kkt_init_state = false;
bool m_setup_done = false;
bool m_enable_iterative_refinement = false;
// residuals
Vec<T> rx;
Vec<T> ry;
Vec<T> rz;
Vec<T> rz_lb;
Vec<T> rz_ub;
Vec<T> rs;
Vec<T> rs_lb;
Vec<T> rs_ub;
// non-regularized residuals
Vec<T> rx_nr;
Vec<T> ry_nr;
Vec<T> rz_nr;
Vec<T> rz_lb_nr;
Vec<T> rz_ub_nr;
// primal and dual steps
Vec<T> dx;
Vec<T> dy;
Vec<T> dz;
Vec<T> dz_lb;
Vec<T> dz_ub;
Vec<T> ds;
Vec<T> ds_lb;
Vec<T> ds_ub;
public:
SolverBase() : m_kkt(m_data, m_settings) {};
~SolverBase() {};
Settings<T>& settings() { return m_settings; }
const Result<T>& result() const { return m_result; }
Status solve()
{
if (m_settings.verbose)
{
piqp_print("----------------------------------------------------------\n");
piqp_print(" PIQP \n");
piqp_print(" (c) Roland Schwan \n");
piqp_print(" Ecole Polytechnique Federale de Lausanne (EPFL) 2024 \n");
piqp_print("----------------------------------------------------------\n");
if (MatrixType == PIQP_DENSE)
{
piqp_print("dense backend\n");
piqp_print("variables n = %zd\n", m_data.n);
piqp_print("equality constraints p = %zd\n", m_data.p);
piqp_print("inequality constraints m = %zd\n", m_data.m);
}
else
{
piqp_print("sparse backend\n");
piqp_print("variables n = %zd, nzz(P upper triangular) = %zd\n", m_data.n, m_data.non_zeros_P_utri());
piqp_print("equality constraints p = %zd, nnz(A) = %zd\n", m_data.p, m_data.non_zeros_A());
piqp_print("inequality constraints m = %zd, nnz(G) = %zd\n", m_data.m, m_data.non_zeros_G());
}
piqp_print("variable lower bounds n_lb = %zd\n", m_data.n_lb);
piqp_print("variable upper bounds n_ub = %zd\n", m_data.n_ub);
piqp_print("\n");
piqp_print("iter prim_obj dual_obj duality_gap prim_inf dual_inf rho delta mu p_step d_step\n");
}
if (m_settings.compute_timings)
{
m_timer.start();
}
Status status = solve_impl();
unscale_results();
restore_box_dual();
if (m_settings.compute_timings)
{
T solve_time = m_timer.stop();
m_result.info.solve_time = solve_time;
m_result.info.run_time += solve_time;
}
if (m_settings.verbose)
{
piqp_print("\n");
piqp_print("status: %s\n", status_to_string(status));
piqp_print("number of iterations: %zd\n", m_result.info.iter);
piqp_print("objective: %.5e\n", (double) m_result.info.primal_obj);
if (m_settings.compute_timings)
{
piqp_print("total run time: %.3es\n", (double) m_result.info.run_time);
piqp_print(" setup time: %.3es\n", (double) m_result.info.setup_time);
piqp_print(" update time: %.3es\n", (double) m_result.info.update_time);
piqp_print(" solve time: %.3es\n", (double) m_result.info.solve_time);
}
}
return status;
}
protected:
void setup_impl(const CMatRefType& P,
const CVecRef<T>& c,
const optional<CMatRefType>& A,
const optional<CVecRef<T>>& b,
const optional<CMatRefType>& G,
const optional<CVecRef<T>>& h,
const optional<CVecRef<T>>& x_lb,
const optional<CVecRef<T>>& x_ub)
{
if (m_settings.compute_timings)
{
m_timer.start();
}
m_data.n = P.rows();
m_data.p = A.has_value() ? A->rows() : 0;
m_data.m = G.has_value() ? G->rows() : 0;
if (P.rows() != m_data.n || P.cols() != m_data.n) { piqp_eprint("P must be square\n"); return; }
if (A.has_value() && (A->rows() != m_data.p || A->cols() != m_data.n)) { piqp_eprint("A must have correct dimensions\n"); return; }
if (G.has_value() && (G->rows() != m_data.m || G->cols() != m_data.n)) { piqp_eprint("G must have correct dimensions\n"); return; }
if (c.size() != m_data.n) { piqp_eprint("c must have correct dimensions\n"); return; }
if ((b.has_value() && b->size() != m_data.p) || (!b.has_value() && m_data.p > 0)) { piqp_eprint("b must have correct dimensions\n"); return; }
if ((h.has_value() && h->size() != m_data.m) || (!h.has_value() && m_data.m > 0)) { piqp_eprint("h must have correct dimensions\n"); return; }
if (x_lb.has_value() && x_lb->size() != m_data.n) { piqp_eprint("x_lb must have correct dimensions\n"); return; }
if (x_ub.has_value() && x_ub->size() != m_data.n) { piqp_eprint("x_ub must have correct dimensions\n"); return; }
m_data.P_utri = P.template triangularView<Eigen::Upper>();
if (A.has_value()) {
m_data.AT = A->transpose();
} else {
m_data.AT.resize(m_data.n, 0);
}
if (G.has_value()) {
m_data.GT = G->transpose();
} else {
m_data.GT.resize(m_data.n, 0);
}
m_data.c = c;
m_data.b = b.has_value() ? *b : Vec<T>::Zero(0);
if (h.has_value()) {
m_data.h = *h;
disable_inf_constraints();
} else {
m_data.h.resize(0);
}
m_data.x_lb_idx.resize(m_data.n);
m_data.x_ub_idx.resize(m_data.n);
m_data.x_lb_scaling = Vec<T>::Constant(m_data.n, T(1));
m_data.x_ub_scaling = Vec<T>::Constant(m_data.n, T(1));
m_data.x_lb_n.resize(m_data.n);
m_data.x_ub.resize(m_data.n);
setup_lb_data(x_lb);
setup_ub_data(x_ub);
init_workspace();
m_preconditioner.init(m_data);
m_preconditioner.scale_data(m_data,
false,
m_settings.preconditioner_scale_cost,
m_settings.preconditioner_iter);
m_kkt.init(m_result.info.rho, m_result.info.delta);
m_kkt_init_state = true;
m_setup_done = true;
m_enable_iterative_refinement = m_settings.iterative_refinement_always_enabled;
if (m_settings.compute_timings)
{
T setup_time = m_timer.stop();
m_result.info.setup_time = setup_time;
m_result.info.run_time += setup_time;
}
}
void disable_inf_constraints()
{
if (m_data.m > 0 && (m_data.h.maxCoeff() > PIQP_INF || m_data.h.minCoeff() < -PIQP_INF))
{
piqp_eprint("h contains values which are close to +/- infinity.\n");
piqp_eprint("PIQP is setting the corresponding rows in G to zero (sparsity preserving).\n");
piqp_eprint("Consider removing the corresponding constraints for faster solves.\n");
for (int i = 0; i < m_data.h.rows(); i++)
{
if (m_data.h(i) > PIQP_INF || m_data.h(i) < -PIQP_INF)
{
m_data.set_G_row_zero(i);
m_data.h(i) = T(1);
}
}
}
}
void setup_lb_data(const optional<CVecRef<T>>& x_lb)
{
isize n_lb = 0;
if (x_lb.has_value())
{
isize i_lb = 0;
for (isize i = 0; i < m_data.n; i++)
{
if ((*x_lb)(i) > -PIQP_INF)
{
n_lb += 1;
m_data.x_lb_n(i_lb) = -(*x_lb)(i);
m_data.x_lb_idx(i_lb) = i;
i_lb++;
}
}
}
m_data.n_lb = n_lb;
}
void setup_ub_data(const optional<CVecRef<T>>& x_ub)
{
isize n_ub = 0;
if (x_ub.has_value())
{
isize i_ub = 0;
for (isize i = 0; i < m_data.n; i++)
{
if ((*x_ub)(i) < PIQP_INF)
{
n_ub += 1;
m_data.x_ub(i_ub) = (*x_ub)(i);
m_data.x_ub_idx(i_ub) = i;
i_ub++;
}
}
}
m_data.n_ub = n_ub;
}
void init_workspace()
{
// init result
m_result.x.resize(m_data.n);
m_result.y.resize(m_data.p);
m_result.z.resize(m_data.m);
m_result.z_lb.resize(m_data.n);
m_result.z_ub.resize(m_data.n);
m_result.s.resize(m_data.m);
m_result.s_lb.resize(m_data.n);
m_result.s_ub.resize(m_data.n);
m_result.zeta.resize(m_data.n);
m_result.lambda.resize(m_data.p);
m_result.nu.resize(m_data.m);
m_result.nu_lb.resize(m_data.n);
m_result.nu_ub.resize(m_data.n);
// init workspace
m_result.info.rho = m_settings.rho_init;
m_result.info.delta = m_settings.delta_init;
m_result.info.setup_time = 0;
m_result.info.update_time = 0;
m_result.info.solve_time = 0;
m_result.info.run_time = 0;
rx.resize(m_data.n);
ry.resize(m_data.p);
rz.resize(m_data.m);
rz_lb.resize(m_data.n);
rz_ub.resize(m_data.n);
rs.resize(m_data.m);
rs_lb.resize(m_data.n);
rs_ub.resize(m_data.n);
rx_nr.resize(m_data.n);
ry_nr.resize(m_data.p);
rz_nr.resize(m_data.m);
rz_lb_nr.resize(m_data.n);
rz_ub_nr.resize(m_data.n);
dx.resize(m_data.n);
dy.resize(m_data.p);
dz.resize(m_data.m);
dz_lb.resize(m_data.n);
dz_ub.resize(m_data.n);
ds.resize(m_data.m);
ds_lb.resize(m_data.n);
ds_ub.resize(m_data.n);
}
Status solve_impl()
{
auto s_lb = m_result.s_lb.head(m_data.n_lb);
auto s_ub = m_result.s_ub.head(m_data.n_ub);
auto z_lb = m_result.z_lb.head(m_data.n_lb);
auto z_ub = m_result.z_ub.head(m_data.n_ub);
auto nu_lb = m_result.nu_lb.head(m_data.n_lb);
auto nu_ub = m_result.nu_ub.head(m_data.n_ub);
if (!m_setup_done)
{
piqp_eprint("Solver not setup yet\n");
m_result.info.status = Status::PIQP_UNSOLVED;
return m_result.info.status;
}
if (!m_settings.verify_settings())
{
m_result.info.status = Status::PIQP_INVALID_SETTINGS;
return m_result.info.status;
}
m_result.info.status = Status::PIQP_UNSOLVED;
m_result.info.iter = 0;
m_result.info.reg_limit = m_settings.reg_lower_limit;
m_result.info.factor_retires = 0;
m_result.info.no_primal_update = 0;
m_result.info.no_dual_update = 0;
m_result.info.mu = 0;
m_result.info.primal_step = 0;
m_result.info.dual_step = 0;
m_result.info.rho = m_settings.rho_init;
m_result.info.delta = m_settings.delta_init;
if (!m_kkt_init_state)
{
m_result.s.setConstant(1);
s_lb.head(m_data.n_lb).setConstant(1);
s_ub.head(m_data.n_ub).setConstant(1);
m_result.z.setConstant(1);
z_lb.head(m_data.n_lb).setConstant(1);
z_ub.head(m_data.n_ub).setConstant(1);
m_kkt.update_scalings(m_result.info.rho, m_result.info.delta,
m_result.s, m_result.s_lb, m_result.s_ub,
m_result.z, m_result.z_lb, m_result.z_ub);
}
else
{
// after solve is called once, the scalings are not in initial state anymore
m_kkt_init_state = false;
}
while (!m_kkt.regularize_and_factorize(m_enable_iterative_refinement))
{
if (!m_enable_iterative_refinement)
{
m_enable_iterative_refinement = true;
}
else if (m_result.info.factor_retires < m_settings.max_factor_retires)
{
m_result.info.delta *= 100;
m_result.info.rho *= 100;
m_result.info.factor_retires++;
m_result.info.reg_limit = std::min(10 * m_result.info.reg_limit, m_settings.eps_abs);
}
else
{
m_result.info.status = Status::PIQP_NUMERICS;
return m_result.info.status;
}
}
m_result.info.factor_retires = 0;
rx = -m_data.c;
// avoid unnecessary copies
// ry = m_data.b;
// rz = m_data.h;
// rz_lb = m_data.x_lb;
// rz_ub = m_data.x_ub;
rs.setZero();
rs_lb.setZero();
rs_ub.setZero();
m_kkt.solve(rx, m_data.b,
m_data.h, m_data.x_lb_n, m_data.x_ub,
rs, rs_lb, rs_ub,
m_result.x, m_result.y,
m_result.z, m_result.z_lb, m_result.z_ub,
m_result.s, m_result.s_lb, m_result.s_ub,
m_enable_iterative_refinement);
if (m_data.m + m_data.n_lb + m_data.n_ub > 0)
{
T s_norm = T(0);
s_norm = std::max(s_norm, m_result.s.template lpNorm<Eigen::Infinity>());
s_norm = std::max(s_norm, s_lb.template lpNorm<Eigen::Infinity>());
s_norm = std::max(s_norm, s_ub.template lpNorm<Eigen::Infinity>());
if (s_norm <= 1e-4)
{
// 0.1 is arbitrary
m_result.s.setConstant(0.1);
s_lb.setConstant(0.1);
s_ub.setConstant(0.1);
m_result.z.setConstant(0.1);
z_lb.setConstant(0.1);
z_ub.setConstant(0.1);
}
T delta_s = T(0);
if (m_data.m > 0) delta_s = std::max(delta_s, -T(1.5) * m_result.s.minCoeff());
if (m_data.n_lb > 0) delta_s = std::max(delta_s, -T(1.5) * s_lb.minCoeff());
if (m_data.n_ub > 0) delta_s = std::max(delta_s, -T(1.5) * s_ub.minCoeff());
T delta_z = T(0);
if (m_data.m > 0) delta_z = std::max(delta_z, -T(1.5) * m_result.z.minCoeff());
if (m_data.n_lb > 0) delta_z = std::max(delta_z, -T(1.5) * z_lb.minCoeff());
if (m_data.n_ub > 0) delta_z = std::max(delta_z, -T(1.5) * z_ub.minCoeff());
T tmp_prod = (m_result.s.array() + delta_s).matrix().dot((m_result.z.array() + delta_z).matrix());
tmp_prod += (s_lb.array() + delta_s).matrix().dot((z_lb.array() + delta_z).matrix());
tmp_prod += (s_ub.array() + delta_s).matrix().dot((z_ub.array() + delta_z).matrix());
T delta_s_bar = delta_s + (T(0.5) * tmp_prod) / (m_result.z.sum() + z_lb.sum() + z_ub.sum() + T(m_data.m + m_data.n_lb + m_data.n_ub) * delta_z);
T delta_z_bar = delta_z + (T(0.5) * tmp_prod) / (m_result.s.sum() + s_lb.sum() + s_ub.sum() + T(m_data.m + m_data.n_lb + m_data.n_ub) * delta_s);
m_result.s.array() += delta_s_bar;
s_lb.array() += delta_s_bar;
s_ub.array() += delta_s_bar;
m_result.z.array() += delta_z_bar;
z_lb.array() += delta_z_bar;
z_ub.array() += delta_z_bar;
m_result.info.mu = (m_result.s.dot(m_result.z) + s_lb.dot(z_lb) + s_ub.dot(z_ub) ) / T(m_data.m + m_data.n_lb + m_data.n_ub);
}
m_result.zeta = m_result.x;
m_result.lambda = m_result.y;
m_result.nu = m_result.z;
nu_lb = z_lb;
nu_ub = z_ub;
while (m_result.info.iter < m_settings.max_iter)
{
if (m_result.info.iter == 0)
{
update_nr_residuals();
}
m_result.info.primal_inf = primal_inf_nr();
m_result.info.dual_inf = dual_inf_nr();
if (m_settings.verbose)
{
piqp_print("%3zd % .5e % .5e %.5e %.5e %.5e %.3e %.3e %.3e %.4f %.4f\n",
m_result.info.iter,
(double) m_result.info.primal_obj,
(double) m_result.info.dual_obj,
(double) m_result.info.duality_gap,
(double) m_result.info.primal_inf,
(double) m_result.info.dual_inf,
(double) m_result.info.rho,
(double) m_result.info.delta,
(double) m_result.info.mu,
(double) m_result.info.primal_step,
(double) m_result.info.dual_step);
}
if (m_result.info.primal_inf < m_settings.eps_abs + m_settings.eps_rel * m_result.info.primal_rel_inf &&
m_result.info.dual_inf < m_settings.eps_abs + m_settings.eps_rel * m_result.info.dual_rel_inf &&
(!m_settings.check_duality_gap || m_result.info.duality_gap < m_settings.eps_duality_gap_abs + m_settings.eps_duality_gap_rel * m_result.info.duality_gap_rel))
{
m_result.info.status = Status::PIQP_SOLVED;
return m_result.info.status;
}
rx = rx_nr - m_result.info.rho * (m_result.x - m_result.zeta);
ry = ry_nr - m_result.info.delta * (m_result.lambda - m_result.y);
rz = rz_nr - m_result.info.delta * (m_result.nu - m_result.z);
rz_lb.head(m_data.n_lb) = rz_lb_nr.head(m_data.n_lb) - m_result.info.delta * (nu_lb.head(m_data.n_lb) - z_lb.head(m_data.n_lb));
rz_ub.head(m_data.n_ub) = rz_ub_nr.head(m_data.n_ub) - m_result.info.delta * (nu_ub.head(m_data.n_ub) - z_ub.head(m_data.n_ub));
if (m_result.info.no_dual_update > std::min(isize(5), m_settings.reg_finetune_dual_update_threshold) &&
primal_prox_inf() > 1e12 &&
primal_inf_r() < m_settings.eps_abs + m_settings.eps_rel * m_result.info.primal_rel_inf)
{
m_result.info.status = Status::PIQP_PRIMAL_INFEASIBLE;
return m_result.info.status;
}
if (m_result.info.no_primal_update > std::min(isize(5), m_settings.reg_finetune_primal_update_threshold) &&
dual_prox_inf() > 1e12 &&
dual_inf_r() < m_settings.eps_abs + m_settings.eps_rel * m_result.info.dual_rel_inf)
{
m_result.info.status = Status::PIQP_DUAL_INFEASIBLE;
return m_result.info.status;
}
m_result.info.iter++;
// avoid getting to close to boundary which can result in a division by zero
bool boundary_shifted = false;
T epsilon = std::numeric_limits<T>::epsilon();
if (m_data.m > 0 && m_result.z.minCoeff() < epsilon)
{
m_result.z.array() += epsilon;
boundary_shifted = true;
}
if (m_data.n_lb > 0 && z_lb.minCoeff() < epsilon)
{
z_lb.array() += epsilon;
boundary_shifted = true;
}
if (m_data.n_ub > 0 && z_ub.minCoeff() < epsilon)
{
z_ub.array() += epsilon;
boundary_shifted = true;
}
if (boundary_shifted)
{
m_result.info.mu = (m_result.s.dot(m_result.z) + s_lb.dot(z_lb) + s_ub.dot(z_ub) ) / T(m_data.m + m_data.n_lb + m_data.n_ub);
}
// avoid possibility of converging to a local minimum -> decrease the minimum regularization value
if ((m_result.info.no_primal_update > m_settings.reg_finetune_primal_update_threshold &&
m_result.info.rho == m_result.info.reg_limit &&
m_result.info.reg_limit != m_settings.reg_finetune_lower_limit) ||
(m_result.info.no_dual_update > m_settings.reg_finetune_dual_update_threshold &&
m_result.info.delta == m_result.info.reg_limit &&
m_result.info.reg_limit != m_settings.reg_finetune_lower_limit))
{
m_result.info.reg_limit = m_settings.reg_finetune_lower_limit;
m_result.info.no_primal_update = 0;
m_result.info.no_dual_update = 0;
}
m_kkt.update_scalings(m_result.info.rho, m_result.info.delta,
m_result.s, m_result.s_lb, m_result.s_ub,
m_result.z, m_result.z_lb, m_result.z_ub);
if (!m_kkt.regularize_and_factorize(m_enable_iterative_refinement))
{
if (!m_enable_iterative_refinement)
{
m_enable_iterative_refinement = true;
continue;
}
else if (m_result.info.factor_retires < m_settings.max_factor_retires)
{
m_result.info.delta *= 100;
m_result.info.rho *= 100;
m_result.info.iter--;
m_result.info.factor_retires++;
m_result.info.reg_limit = std::min(10 * m_result.info.reg_limit, m_settings.eps_abs);
continue;
}
else
{
m_result.info.status = Status::PIQP_NUMERICS;
return m_result.info.status;
}
}
m_result.info.factor_retires = 0;
if (m_data.m + m_data.n_lb + m_data.n_ub > 0)
{
// ------------------ predictor step ------------------
rs.array() = -m_result.s.array() * m_result.z.array();
rs_lb.head(m_data.n_lb).array() = -s_lb.array() * z_lb.array();
rs_ub.head(m_data.n_ub).array() = -s_ub.array() * z_ub.array();
m_kkt.solve(rx, ry, rz, rz_lb, rz_ub, rs, rs_lb, rs_ub,
dx, dy, dz, dz_lb, dz_ub, ds, ds_lb, ds_ub,
m_enable_iterative_refinement);
// step in the non-negative orthant
T alpha_s = T(1);
T alpha_z = T(1);
for (isize i = 0; i < m_data.m; i++)
{
if (ds(i) < 0)
{
alpha_s = std::min(alpha_s, -m_result.s(i) / ds(i));
}
if (dz(i) < 0)
{
alpha_z = std::min(alpha_z, -m_result.z(i) / dz(i));
}
}
for (isize i = 0; i < m_data.n_lb; i++)
{
if (ds_lb(i) < 0)
{
alpha_s = std::min(alpha_s, -m_result.s_lb(i) / ds_lb(i));
}
if (dz_lb(i) < 0)
{
alpha_z = std::min(alpha_z, -m_result.z_lb(i) / dz_lb(i));
}
}
for (isize i = 0; i < m_data.n_ub; i++)
{
if (ds_ub(i) < 0)
{
alpha_s = std::min(alpha_s, -m_result.s_ub(i) / ds_ub(i));
}
if (dz_ub(i) < 0)
{
alpha_z = std::min(alpha_z, -m_result.z_ub(i) / dz_ub(i));
}
}
// avoid getting to close to the boundary
alpha_s *= m_settings.tau;
alpha_z *= m_settings.tau;
m_result.info.sigma = (m_result.s + alpha_s * ds).dot(m_result.z + alpha_z * dz);
m_result.info.sigma += (s_lb + alpha_s * ds_lb.head(m_data.n_lb)).dot(z_lb + alpha_z * dz_lb.head(m_data.n_lb));
m_result.info.sigma += (s_ub + alpha_s * ds_ub.head(m_data.n_ub)).dot(z_ub + alpha_z * dz_ub.head(m_data.n_ub));
m_result.info.sigma /= (m_result.info.mu * T(m_data.m + m_data.n_lb + m_data.n_ub));
m_result.info.sigma = std::max(T(0), std::min(T(1), m_result.info.sigma));
m_result.info.sigma = m_result.info.sigma * m_result.info.sigma * m_result.info.sigma;
// ------------------ corrector step ------------------
rs.array() += -ds.array() * dz.array() + m_result.info.sigma * m_result.info.mu;
rs_lb.head(m_data.n_lb).array() += -ds_lb.head(m_data.n_lb).array() * dz_lb.head(m_data.n_lb).array() + m_result.info.sigma * m_result.info.mu;
rs_ub.head(m_data.n_ub).array() += -ds_ub.head(m_data.n_ub).array() * dz_ub.head(m_data.n_ub).array() + m_result.info.sigma * m_result.info.mu;
m_kkt.solve(rx, ry, rz, rz_lb, rz_ub, rs, rs_lb, rs_ub,
dx, dy, dz, dz_lb, dz_ub, ds, ds_lb, ds_ub,
m_enable_iterative_refinement);
// step in the non-negative orthant
alpha_s = T(1);
alpha_z = T(1);
for (isize i = 0; i < m_data.m; i++)
{
if (ds(i) < 0)
{
alpha_s = std::min(alpha_s, -m_result.s(i) / ds(i));
}
if (dz(i) < 0)
{
alpha_z = std::min(alpha_z, -m_result.z(i) / dz(i));
}
}
for (isize i = 0; i < m_data.n_lb; i++)
{
if (ds_lb(i) < 0)
{
alpha_s = std::min(alpha_s, -m_result.s_lb(i) / ds_lb(i));
}
if (dz_lb(i) < 0)
{
alpha_z = std::min(alpha_z, -m_result.z_lb(i) / dz_lb(i));
}
}
for (isize i = 0; i < m_data.n_ub; i++)
{
if (ds_ub(i) < 0)
{
alpha_s = std::min(alpha_s, -m_result.s_ub(i) / ds_ub(i));
}
if (dz_ub(i) < 0)
{
alpha_z = std::min(alpha_z, -m_result.z_ub(i) / dz_ub(i));
}
}
// avoid getting to close to the boundary
m_result.info.primal_step = alpha_s * m_settings.tau;
m_result.info.dual_step = alpha_z * m_settings.tau;
// ------------------ update ------------------
m_result.x += m_result.info.primal_step * dx;
m_result.y += m_result.info.dual_step * dy;
m_result.z += m_result.info.dual_step * dz;
z_lb += m_result.info.dual_step * dz_lb.head(m_data.n_lb);
z_ub += m_result.info.dual_step * dz_ub.head(m_data.n_ub);
m_result.s += m_result.info.primal_step * ds;
s_lb += m_result.info.primal_step * ds_lb.head(m_data.n_lb);
s_ub += m_result.info.primal_step * ds_ub.head(m_data.n_ub);
T mu_prev = m_result.info.mu;
m_result.info.mu = (m_result.s.dot(m_result.z) + s_lb.dot(z_lb) + s_ub.dot(z_ub) ) / T(m_data.m + m_data.n_lb + m_data.n_ub);
T mu_rate = std::max(T(0), (mu_prev - m_result.info.mu) / mu_prev);
// ------------------ update regularization ------------------
update_nr_residuals();
if (dual_inf_nr() < 0.95 * m_result.info.dual_inf || (m_result.info.rho == m_settings.reg_finetune_lower_limit && dual_prox_inf() < 1e2))
{
m_result.zeta = m_result.x;
m_result.info.rho = std::max(m_result.info.reg_limit, (T(1) - mu_rate) * m_result.info.rho);
}
else
{
m_result.info.no_primal_update++;
m_result.info.rho = std::max(m_result.info.reg_limit, (T(1) - T(0.666) * mu_rate) * m_result.info.rho);
}
if (primal_inf_nr() < 0.95 * m_result.info.primal_inf || (m_result.info.delta == m_settings.reg_finetune_lower_limit && primal_prox_inf() < 1e2))
{
m_result.lambda = m_result.y;
m_result.nu = m_result.z;
nu_lb = z_lb;
nu_ub = z_ub;
m_result.info.delta = std::max(m_result.info.reg_limit, (T(1) - mu_rate) * m_result.info.delta);
}
else
{
m_result.info.no_dual_update++;
m_result.info.delta = std::max(m_result.info.reg_limit, (T(1) - T(0.666) * mu_rate) * m_result.info.delta);
}
}
else
{
// since there are no inequalities we can take full steps
m_kkt.solve(rx, ry, rz, rz_lb, rz_ub, rs, rs_lb, rs_ub,
dx, dy, dz, dz_lb, dz_ub, ds, ds_lb, ds_ub,
m_enable_iterative_refinement);
m_result.info.primal_step = T(1);
m_result.info.dual_step = T(1);
m_result.x += m_result.info.primal_step * dx;
m_result.y += m_result.info.dual_step * dy;
// ------------------ update regularization ------------------
update_nr_residuals();
if (dual_inf_nr() < 0.95 * m_result.info.dual_inf)
{
m_result.zeta = m_result.x;
m_result.info.rho = std::max(m_result.info.reg_limit, T(0.1) * m_result.info.rho);
}
else
{
m_result.info.no_primal_update++;
m_result.info.rho = std::max(m_result.info.reg_limit, T(0.5) * m_result.info.rho);
}
if (primal_inf_nr() < 0.95 * m_result.info.primal_inf)
{
m_result.lambda = m_result.y;
m_result.info.delta = std::max(m_result.info.reg_limit, T(0.1) * m_result.info.delta);
}
else
{
m_result.info.no_dual_update++;
m_result.info.delta = std::max(m_result.info.reg_limit, T(0.5) * m_result.info.delta);
}
}
}
m_result.info.status = Status::PIQP_MAX_ITER_REACHED;
return m_result.info.status;
}
void update_nr_residuals()
{
using std::abs;
// first part of dual residual and infeasibility calculation (used in cost calculation)
rx_nr.noalias() = -m_data.P_utri * m_result.x;
rx_nr.noalias() -= m_data.P_utri.transpose().template triangularView<Eigen::StrictlyLower>() * m_result.x;
m_result.info.dual_rel_inf = m_preconditioner.unscale_dual_res(rx_nr).template lpNorm<Eigen::Infinity>();
// calculate primal cost, dual cost, and duality gap
T tmp = -m_result.x.dot(rx_nr); // x'Px
m_result.info.primal_obj = T(0.5) * tmp;
m_result.info.dual_obj = -T(0.5) * tmp;
m_result.info.duality_gap_rel = m_preconditioner.unscale_cost(abs(tmp));
tmp = m_data.c.dot(m_result.x);
m_result.info.primal_obj += tmp;
m_result.info.duality_gap_rel = std::max(m_result.info.duality_gap_rel, m_preconditioner.unscale_cost(abs(tmp)));
tmp = m_data.b.dot(m_result.y);
m_result.info.dual_obj -= tmp;
m_result.info.duality_gap_rel = std::max(m_result.info.duality_gap_rel, m_preconditioner.unscale_cost(abs(tmp)));
tmp = m_data.h.dot(m_result.z);
m_result.info.dual_obj -= tmp;
m_result.info.duality_gap_rel = std::max(m_result.info.duality_gap_rel, m_preconditioner.unscale_cost(abs(tmp)));
tmp = m_data.x_lb_n.head(m_data.n_lb).dot(m_result.z_lb.head(m_data.n_lb));
m_result.info.dual_obj -= tmp;
m_result.info.duality_gap_rel = std::max(m_result.info.duality_gap_rel, m_preconditioner.unscale_cost(abs(tmp)));
tmp = m_data.x_ub.head(m_data.n_ub).dot(m_result.z_ub.head(m_data.n_ub));
m_result.info.dual_obj -= tmp;
m_result.info.duality_gap_rel = std::max(m_result.info.duality_gap_rel, m_preconditioner.unscale_cost(abs(tmp)));
m_result.info.duality_gap = abs(m_result.info.primal_obj - m_result.info.dual_obj);
m_result.info.primal_obj = m_preconditioner.unscale_cost(m_result.info.primal_obj);
m_result.info.dual_obj = m_preconditioner.unscale_cost(m_result.info.dual_obj);
m_result.info.duality_gap = m_preconditioner.unscale_cost(m_result.info.duality_gap);
// dual residual and infeasibility calculation
rx_nr.noalias() -= m_data.c;
m_result.info.dual_rel_inf = std::max(m_result.info.dual_rel_inf, m_preconditioner.unscale_dual_res(m_data.c).template lpNorm<Eigen::Infinity>());
dx.noalias() = m_data.AT * m_result.y; // use dx as a temporary
dx.noalias() += m_data.GT * m_result.z;
for (isize i = 0; i < m_data.n_lb; i++)
{
dx(m_data.x_lb_idx(i)) -= m_data.x_lb_scaling(i) * m_result.z_lb(i);
}
for (isize i = 0; i < m_data.n_ub; i++)
{
dx(m_data.x_ub_idx(i)) += m_data.x_ub_scaling(i) * m_result.z_ub(i);
}
m_result.info.dual_rel_inf = std::max(m_result.info.dual_rel_inf, m_preconditioner.unscale_dual_res(dx).template lpNorm<Eigen::Infinity>());
rx_nr.noalias() -= dx;
// primal residual and infeasibility calculation
ry_nr.noalias() = -m_data.AT.transpose() * m_result.x;
m_result.info.primal_rel_inf = m_preconditioner.unscale_primal_res_eq(ry_nr).template lpNorm<Eigen::Infinity>();
ry_nr.noalias() += m_data.b;
m_result.info.primal_rel_inf = std::max(m_result.info.primal_rel_inf, m_preconditioner.unscale_primal_res_eq(m_data.b).template lpNorm<Eigen::Infinity>());
rz_nr.noalias() = -m_data.GT.transpose() * m_result.x;
m_result.info.primal_rel_inf = std::max(m_result.info.primal_rel_inf, m_preconditioner.unscale_primal_res_ineq(rz_nr).template lpNorm<Eigen::Infinity>());
rz_nr.noalias() += m_data.h - m_result.s;
m_result.info.primal_rel_inf = std::max(m_result.info.primal_rel_inf, m_preconditioner.unscale_primal_res_ineq(m_data.h).template lpNorm<Eigen::Infinity>());
m_result.info.primal_rel_inf = std::max(m_result.info.primal_rel_inf, m_preconditioner.unscale_primal_res_ineq(m_result.s).template lpNorm<Eigen::Infinity>());
for (isize i = 0; i < m_data.n_lb; i++)
{
rz_lb_nr(i) = m_data.x_lb_scaling(i) * m_result.x(m_data.x_lb_idx(i));
}
m_result.info.primal_rel_inf = std::max(m_result.info.primal_rel_inf, m_preconditioner.unscale_primal_res_lb(rz_lb_nr.head(m_data.n_lb)).template lpNorm<Eigen::Infinity>());
rz_lb_nr.head(m_data.n_lb).noalias() += m_data.x_lb_n.head(m_data.n_lb) - m_result.s_lb.head(m_data.n_lb);
m_result.info.primal_rel_inf = std::max(m_result.info.primal_rel_inf, m_preconditioner.unscale_primal_res_lb(m_data.x_lb_n.head(m_data.n_lb)).template lpNorm<Eigen::Infinity>());
m_result.info.primal_rel_inf = std::max(m_result.info.primal_rel_inf, m_preconditioner.unscale_primal_res_lb(m_result.s_lb.head(m_data.n_lb)).template lpNorm<Eigen::Infinity>());
for (isize i = 0; i < m_data.n_ub; i++)
{
rz_ub_nr(i) = -m_data.x_ub_scaling(i) * m_result.x(m_data.x_ub_idx(i));
}
m_result.info.primal_rel_inf = std::max(m_result.info.primal_rel_inf, m_preconditioner.unscale_primal_res_ub(rz_ub_nr.head(m_data.n_ub)).template lpNorm<Eigen::Infinity>());
rz_ub_nr.head(m_data.n_ub).noalias() += m_data.x_ub.head(m_data.n_ub) - m_result.s_ub.head(m_data.n_ub);
m_result.info.primal_rel_inf = std::max(m_result.info.primal_rel_inf, m_preconditioner.unscale_primal_res_ub(m_data.x_ub.head(m_data.n_ub)).template lpNorm<Eigen::Infinity>());
m_result.info.primal_rel_inf = std::max(m_result.info.primal_rel_inf, m_preconditioner.unscale_primal_res_ub(m_result.s_ub.head(m_data.n_ub)).template lpNorm<Eigen::Infinity>());
}
T primal_inf_nr()
{
T inf = m_preconditioner.unscale_primal_res_eq(ry_nr).template lpNorm<Eigen::Infinity>();
inf = std::max(inf, m_preconditioner.unscale_primal_res_ineq(rz_nr).template lpNorm<Eigen::Infinity>());
inf = std::max(inf, m_preconditioner.unscale_primal_res_lb(rz_lb_nr.head(m_data.n_lb)).template lpNorm<Eigen::Infinity>());
inf = std::max(inf, m_preconditioner.unscale_primal_res_ub(rz_ub_nr.head(m_data.n_ub)).template lpNorm<Eigen::Infinity>());
return inf;
}
T primal_inf_r()
{
T inf = m_preconditioner.unscale_primal_res_eq(ry).template lpNorm<Eigen::Infinity>();
inf = std::max(inf, m_preconditioner.unscale_primal_res_ineq(rz).template lpNorm<Eigen::Infinity>());
inf = std::max(inf, m_preconditioner.unscale_primal_res_lb(rz_lb.head(m_data.n_lb)).template lpNorm<Eigen::Infinity>());
inf = std::max(inf, m_preconditioner.unscale_primal_res_ub(rz_ub.head(m_data.n_ub)).template lpNorm<Eigen::Infinity>());
return inf;
}
T primal_prox_inf()
{
T inf = m_preconditioner.unscale_dual_eq(m_result.lambda - m_result.y).template lpNorm<Eigen::Infinity>();
inf = std::max(inf, m_preconditioner.unscale_dual_ineq(m_result.nu - m_result.z).template lpNorm<Eigen::Infinity>());
inf = std::max(inf, m_preconditioner.unscale_dual_lb(m_result.nu_lb.head(m_data.n_lb) - m_result.z_lb.head(m_data.n_lb)).template lpNorm<Eigen::Infinity>());
inf = std::max(inf, m_preconditioner.unscale_dual_ub(m_result.nu_ub.head(m_data.n_ub) - m_result.z_ub.head(m_data.n_ub)).template lpNorm<Eigen::Infinity>());
return inf;
}
T dual_inf_nr()
{
return m_preconditioner.unscale_dual_res(rx_nr).template lpNorm<Eigen::Infinity>();
}
T dual_inf_r()
{
return m_preconditioner.unscale_dual_res(rx).template lpNorm<Eigen::Infinity>();
}
T dual_prox_inf()
{
return m_preconditioner.unscale_primal(m_result.x - m_result.zeta).template lpNorm<Eigen::Infinity>();
}
void restore_box_dual()
{
m_result.z_lb.tail(m_data.n - m_data.n_lb).setZero();
m_result.z_ub.tail(m_data.n - m_data.n_ub).setZero();
m_result.s_lb.tail(m_data.n - m_data.n_lb).array() = std::numeric_limits<T>::infinity();
m_result.s_ub.tail(m_data.n - m_data.n_ub).array() = std::numeric_limits<T>::infinity();
m_result.nu_lb.tail(m_data.n - m_data.n_lb).setZero();
m_result.nu_ub.tail(m_data.n - m_data.n_ub).setZero();
for (isize i = m_data.n_lb - 1; i >= 0; i--)
{
std::swap(m_result.z_lb(i), m_result.z_lb(m_data.x_lb_idx(i)));
std::swap(m_result.s_lb(i), m_result.s_lb(m_data.x_lb_idx(i)));
std::swap(m_result.nu_lb(i), m_result.nu_lb(m_data.x_lb_idx(i)));
}
for (isize i = m_data.n_ub - 1; i >= 0; i--)
{
std::swap(m_result.z_ub(i), m_result.z_ub(m_data.x_ub_idx(i)));
std::swap(m_result.s_ub(i), m_result.s_ub(m_data.x_ub_idx(i)));
std::swap(m_result.nu_ub(i), m_result.nu_ub(m_data.x_ub_idx(i)));
}
}
void unscale_results()
{
m_result.x = m_preconditioner.unscale_primal(m_result.x);
m_result.y = m_preconditioner.unscale_dual_eq(m_result.y);
m_result.z = m_preconditioner.unscale_dual_ineq(m_result.z);
m_result.z_lb.head(m_data.n_lb) = m_preconditioner.unscale_dual_lb(m_result.z_lb.head(m_data.n_lb));
m_result.z_ub.head(m_data.n_ub) = m_preconditioner.unscale_dual_ub(m_result.z_ub.head(m_data.n_ub));
m_result.s = m_preconditioner.unscale_slack_ineq(m_result.s);
m_result.s_lb.head(m_data.n_lb) = m_preconditioner.unscale_slack_lb(m_result.s_lb.head(m_data.n_lb));
m_result.s_ub.head(m_data.n_ub) = m_preconditioner.unscale_slack_ub(m_result.s_ub.head(m_data.n_ub));
m_result.zeta = m_preconditioner.unscale_primal(m_result.zeta);
m_result.lambda = m_preconditioner.unscale_dual_eq(m_result.lambda);
m_result.nu = m_preconditioner.unscale_dual_ineq(m_result.nu);
m_result.nu_lb.head(m_data.n_lb) = m_preconditioner.unscale_dual_lb(m_result.nu_lb.head(m_data.n_lb));
m_result.nu_ub.head(m_data.n_ub) = m_preconditioner.unscale_dual_ub(m_result.nu_ub.head(m_data.n_ub));
}
};
template<typename T, typename Preconditioner = dense::RuizEquilibration<T>>
class DenseSolver : public SolverBase<DenseSolver<T, Preconditioner>, T, int, Preconditioner, PIQP_DENSE, KKTMode::KKT_FULL>
{
public:
void setup(const CMatRef<T>& P,
const CVecRef<T>& c,
const optional<CMatRef<T>>& A = nullopt,
const optional<CVecRef<T>>& b = nullopt,
const optional<CMatRef<T>>& G = nullopt,
const optional<CVecRef<T>>& h = nullopt,
const optional<CVecRef<T>>& x_lb = nullopt,
const optional<CVecRef<T>>& x_ub = nullopt)
{
this->setup_impl(P, c, A, b, G, h, x_lb, x_ub);
}
void update(const optional<CMatRef<T>>& P = nullopt,
const optional<CVecRef<T>>& c = nullopt,
const optional<CMatRef<T>>& A = nullopt,
const optional<CVecRef<T>>& b = nullopt,
const optional<CMatRef<T>>& G = nullopt,
const optional<CVecRef<T>>& h = nullopt,
const optional<CVecRef<T>>& x_lb = nullopt,
const optional<CVecRef<T>>& x_ub = nullopt,
bool reuse_preconditioner = true)
{
if (!this->m_setup_done)
{
piqp_eprint("Solver not setup yet\n");
return;
}
if (this->m_settings.compute_timings)
{
this->m_timer.start();
}