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210 lines
7.2 KiB
210 lines
7.2 KiB
/* -*- c++ -*- (enables emacs c++ mode) */
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/*===========================================================================
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Copyright (C) 2004-2017 Yves Renard
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This file is a part of GetFEM++
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GetFEM++ is free software; you can redistribute it and/or modify it
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under the terms of the GNU Lesser General Public License as published
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by the Free Software Foundation; either version 3 of the License, or
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(at your option) any later version along with the GCC Runtime Library
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Exception either version 3.1 or (at your option) any later version.
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This program is distributed in the hope that it will be useful, but
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WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
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or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public
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License and GCC Runtime Library Exception for more details.
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You should have received a copy of the GNU Lesser General Public License
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along with this program; if not, write to the Free Software Foundation,
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Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301, USA.
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As a special exception, you may use this file as it is a part of a free
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software library without restriction. Specifically, if other files
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instantiate templates or use macros or inline functions from this file,
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or you compile this file and link it with other files to produce an
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executable, this file does not by itself cause the resulting executable
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to be covered by the GNU Lesser General Public License. This exception
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does not however invalidate any other reasons why the executable file
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might be covered by the GNU Lesser General Public License.
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===========================================================================*/
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/**@file gmm_solver_bfgs.h
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@author Yves Renard <Yves.Renard@insa-lyon.fr>
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@date October 14 2004.
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@brief Implements BFGS (Broyden, Fletcher, Goldfarb, Shanno) algorithm.
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*/
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#ifndef GMM_BFGS_H
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#define GMM_BFGS_H
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#include "gmm_kernel.h"
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#include "gmm_iter.h"
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namespace gmm {
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// BFGS algorithm (Broyden, Fletcher, Goldfarb, Shanno)
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// Quasi Newton method for optimization problems.
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// with Wolfe Line search.
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// delta[k] = x[k+1] - x[k]
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// gamma[k] = grad f(x[k+1]) - grad f(x[k])
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// H[0] = I
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// BFGS : zeta[k] = delta[k] - H[k] gamma[k]
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// DFP : zeta[k] = H[k] gamma[k]
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// tau[k] = gamma[k]^T zeta[k]
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// rho[k] = 1 / gamma[k]^T delta[k]
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// BFGS : H[k+1] = H[k] + rho[k](zeta[k] delta[k]^T + delta[k] zeta[k]^T)
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// - rho[k]^2 tau[k] delta[k] delta[k]^T
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// DFP : H[k+1] = H[k] + rho[k] delta[k] delta[k]^T
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// - (1/tau[k])zeta[k] zeta[k]^T
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// Object representing the inverse of the Hessian
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template <typename VECTOR> struct bfgs_invhessian {
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typedef typename linalg_traits<VECTOR>::value_type T;
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typedef typename number_traits<T>::magnitude_type R;
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std::vector<VECTOR> delta, gamma, zeta;
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std::vector<T> tau, rho;
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int version;
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template<typename VEC1, typename VEC2> void hmult(const VEC1 &X, VEC2 &Y) {
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copy(X, Y);
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for (size_type k = 0 ; k < delta.size(); ++k) {
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T xdelta = vect_sp(X, delta[k]), xzeta = vect_sp(X, zeta[k]);
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switch (version) {
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case 0 : // BFGS
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add(scaled(zeta[k], rho[k]*xdelta), Y);
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add(scaled(delta[k], rho[k]*(xzeta-rho[k]*tau[k]*xdelta)), Y);
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break;
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case 1 : // DFP
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add(scaled(delta[k], rho[k]*xdelta), Y);
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add(scaled(zeta[k], -xzeta/tau[k]), Y);
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break;
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}
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}
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}
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void restart(void) {
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delta.resize(0); gamma.resize(0); zeta.resize(0);
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tau.resize(0); rho.resize(0);
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}
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template<typename VECT1, typename VECT2>
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void update(const VECT1 &deltak, const VECT2 &gammak) {
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T vsp = vect_sp(deltak, gammak);
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if (vsp == T(0)) return;
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size_type N = vect_size(deltak), k = delta.size();
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VECTOR Y(N);
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hmult(gammak, Y);
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delta.resize(k+1); gamma.resize(k+1); zeta.resize(k+1);
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tau.resize(k+1); rho.resize(k+1);
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resize(delta[k], N); resize(gamma[k], N); resize(zeta[k], N);
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gmm::copy(deltak, delta[k]);
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gmm::copy(gammak, gamma[k]);
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rho[k] = R(1) / vsp;
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if (version == 0)
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add(delta[k], scaled(Y, -1), zeta[k]);
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else
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gmm::copy(Y, zeta[k]);
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tau[k] = vect_sp(gammak, zeta[k]);
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}
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bfgs_invhessian(int v = 0) { version = v; }
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};
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template <typename FUNCTION, typename DERIVATIVE, typename VECTOR>
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void bfgs(const FUNCTION &f, const DERIVATIVE &grad, VECTOR &x,
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int restart, iteration& iter, int version = 0,
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double lambda_init=0.001, double print_norm=1.0) {
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typedef typename linalg_traits<VECTOR>::value_type T;
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typedef typename number_traits<T>::magnitude_type R;
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bfgs_invhessian<VECTOR> invhessian(version);
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VECTOR r(vect_size(x)), d(vect_size(x)), y(vect_size(x)), r2(vect_size(x));
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grad(x, r);
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R lambda = lambda_init, valx = f(x), valy;
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int nb_restart(0);
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if (iter.get_noisy() >= 1) cout << "value " << valx / print_norm << " ";
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while (! iter.finished_vect(r)) {
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invhessian.hmult(r, d); gmm::scale(d, T(-1));
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// Wolfe Line search
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R derivative = gmm::vect_sp(r, d);
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R lambda_min(0), lambda_max(0), m1 = 0.27, m2 = 0.57;
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bool unbounded = true, blocked = false, grad_computed = false;
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for(;;) {
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add(x, scaled(d, lambda), y);
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valy = f(y);
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if (iter.get_noisy() >= 2) {
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cout.precision(15);
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cout << "Wolfe line search, lambda = " << lambda
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<< " value = " << valy /print_norm << endl;
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// << " derivative = " << derivative
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// << " lambda min = " << lambda_min << " lambda max = "
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// << lambda_max << endl; getchar();
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}
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if (valy <= valx + m1 * lambda * derivative) {
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grad(y, r2); grad_computed = true;
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T derivative2 = gmm::vect_sp(r2, d);
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if (derivative2 >= m2*derivative) break;
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lambda_min = lambda;
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}
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else {
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lambda_max = lambda;
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unbounded = false;
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}
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if (unbounded) lambda *= R(10);
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else lambda = (lambda_max + lambda_min) / R(2);
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if (lambda == lambda_max || lambda == lambda_min) break;
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// valy <= R(2)*valx replaced by
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// valy <= valx + gmm::abs(derivative)*lambda_init
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// for compatibility with negative values (08.24.07).
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if (valy <= valx + R(2)*gmm::abs(derivative)*lambda &&
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(lambda < R(lambda_init*1E-8) ||
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(!unbounded && lambda_max-lambda_min < R(lambda_init*1E-8))))
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{ blocked = true; lambda = lambda_init; break; }
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}
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// Rank two update
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++iter;
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if (!grad_computed) grad(y, r2);
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gmm::add(scaled(r2, -1), r);
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if ((iter.get_iteration() % restart) == 0 || blocked) {
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if (iter.get_noisy() >= 1) cout << "Restart\n";
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invhessian.restart();
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if (++nb_restart > 10) {
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if (iter.get_noisy() >= 1) cout << "BFGS is blocked, exiting\n";
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return;
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}
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}
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else {
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invhessian.update(gmm::scaled(d,lambda), gmm::scaled(r,-1));
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nb_restart = 0;
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}
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copy(r2, r); copy(y, x); valx = valy;
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if (iter.get_noisy() >= 1)
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cout << "BFGS value " << valx/print_norm << "\t";
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}
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}
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template <typename FUNCTION, typename DERIVATIVE, typename VECTOR>
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inline void dfp(const FUNCTION &f, const DERIVATIVE &grad, VECTOR &x,
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int restart, iteration& iter, int version = 1) {
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bfgs(f, grad, x, restart, iter, version);
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}
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}
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#endif
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