/usr/include/trilinos/FeasibleNewton.hpp is in libtrilinos-dev 10.4.0.dfsg-1ubuntu2.
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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 | /* *****************************************************************
MESQUITE -- The Mesh Quality Improvement Toolkit
Copyright 2004 Sandia Corporation and Argonne National
Laboratory. Under the terms of Contract DE-AC04-94AL85000
with Sandia Corporation, the U.S. Government retains certain
rights in this software.
This library 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 2.1 of the License, or (at your option) any later version.
This library 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
(lgpl.txt) along with this library; if not, write to the Free Software
Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
diachin2@llnl.gov, djmelan@sandia.gov, mbrewer@sandia.gov,
pknupp@sandia.gov, tleurent@mcs.anl.gov, tmunson@mcs.anl.gov
***************************************************************** */
// -*- Mode : c++; tab-width: 3; c-tab-always-indent: t; indent-tabs-mode: nil; c-basic-offset: 3 -*-
//
// AUTHOR: Thomas Leurent <tleurent@mcs.anl.gov>
// ORG: Argonne National Laboratory
// E-MAIL: tleurent@mcs.anl.gov
//
// ORIG-DATE: 15-Jan-03 at 08:05:56
// LAST-MOD: 23-May-03 at 11:20:14 by Thomas Leurent
//
// DESCRIPTION:
// ============
/*!
\file FeasibleNewton.hpp
\brief
The FeasibleNewton Class implements the newton non-linear programming algorythm
in order to move a free vertex to an optimal position given an
ObjectiveFunction object and a QualityMetric object.
\author Thomas Leurent
\author Todd Munson
\date 2003-01-15
*/
// DESCRIP-END.
//
#ifndef MSQ_FeasibleNewton_hpp
#define MSQ_FeasibleNewton_hpp
#include "Mesquite.hpp"
#include "VertexMover.hpp"
#include "MsqHessian.hpp"
#include "PatchSetUser.hpp"
namespace MESQUITE_NS
{
class ObjectiveFunction;
/*! \class FeasibleNewton
\brief High Performance implementation of the Feasible Newton algorythm.
Consider our non-linear objective function
\f$ f: I\!\!R^{3N} \rightarrow I\!\!R \f$ where \f$ N \f$
is the number of vertices of the mesh, and \f$ 3N \f$ is therefore the number
of degrees of freedom of the mesh.
The Taylor expansion of \f$ f \f$ around the point \f$ x_0 \f$ is
\f[ f(x_0+d) = f(x_0) + \nabla f(x_0)d + \frac{1}{2} d^T\nabla^2 f(x_0)d
+ ... \;\;\; .\f]
Each iteration of the Newton algorithm tries to find a descent vector that
minimizes the above quadratic approximation, i.e. it looks for
\f[ \min_{d} q(d;x_0) = f(x_0) + \nabla f(x_0)d + \frac{1}{2} d^T\nabla^2 f(x_0)d
\;\; . \f]
We know that if a quadratic function has a finite minimum, it is reached at the
point where the function gradient is null and that the function Hessian
is then positive definite.
Therefore we are looking for \f$ d \f$ such that \f$ \nabla q(d;x_0) =0 \f$. We have
\f[ \nabla q(d;x_0) = \nabla f(x_0) + \nabla^2 f(x_0)d \;\;, \f]
therefore we must solve for \f$ d \f$ the system
\f[ \nabla^2 f(x_0)d = -\nabla f(x_0) \;\; . \f]
We assume that the Hessian is positive definite and we use the conjugate gradient
algebraic solver to solve the above system. If the conjugate gradient solver finds
a direction of negative curvature, the Hessian was not positive definite and we take
a step in that direction of negative curvature, which is a descent direction.
*/
class FeasibleNewton : public VertexMover, public PatchSetUser
{
public:
MESQUITE_EXPORT FeasibleNewton(ObjectiveFunction* of, bool Nash = true);
MESQUITE_EXPORT virtual ~FeasibleNewton()
{ delete coordsMem; }
/*! Sets a minimum value for the gradient. If the gradient is below that value,
we stop iterating. */
MESQUITE_EXPORT void set_lower_gradient_bound(double gradc){
convTol=gradc;}
PatchSet* get_patch_set();
MESQUITE_EXPORT std::string get_name() const;
protected:
virtual void initialize(PatchData &pd, MsqError &err);
virtual void optimize_vertex_positions(PatchData &pd,
MsqError &err);
virtual void initialize_mesh_iteration(PatchData &pd, MsqError &err);
virtual void terminate_mesh_iteration(PatchData &pd, MsqError &err);
virtual void cleanup();
private:
double convTol;
MsqHessian mHessian;
PatchDataVerticesMemento* coordsMem;
bool havePrintedDirectionMessage;
};
}
#endif // MSQ_FeasibleNewton_hpp
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