libtrilinos-nox-dev 12.4.2-2 / usr / include / trilinos / NOX_Solver_TrustRegionBased.H

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#ifndef NOX_SOLVER_TRUSTREGIONBASED_H
#define NOX_SOLVER_TRUSTREGIONBASED_H

#include "NOX_Solver_Generic.H"	        // base class
#include "Teuchos_ParameterList.hpp"	// class data element
#include "NOX_Utils.H"	                // class data element
#include "NOX_Solver_PrePostOperator.H" // class data element

// Forward declaration
namespace NOX {
  class GlobalData;
  namespace MeritFunction {
    class Generic;
  }
  namespace Direction {
    class Generic;
  }
}

namespace NOX {
namespace Solver {

/*!
  \brief %Newton-like solver using a trust region.

Our goal is to solve: \f$ F(x) = 0, \f$ where \f$ F:\Re^n \rightarrow
\Re^n \f$.  Alternatively, we might say that we wish to solve

  
\f$
\min f(x) \equiv \frac{1}{2} \|F(x)\|^2_2.
\f$

The trust region subproblem (TRSP) at iteration \f$k\f$ is given by

  
\f$
\min \; m_k(s) \equiv f_k + g_k^T d + \frac{1}{2} d^T B_k d,
\mbox{ s.t. } \|d\| \leq \Delta_k
\quad \mbox{(TRSP)}
\f$

where

<ul>
<li>\f$ f_k = f(x_k) = \frac{1}{2} \|F(x_k)\|^2_2 \f$,
<li>\f$ g_k = \nabla f(x_k) = J(x_k)^T F(x_k) \f$,
<li>\f$ B_k =  J(x_k)^T J(x_k) \approx \nabla^2 f(x_k) \f$,
<li>\f$ J(x_k)\f$ is the Jacobian of \f$F\f$ at \f$x_k\f$, and
<li>\f$ \Delta_k \f$ is the trust region radius.
</ul>

The "improvement ratio" for a given step \f$ s \f$ is defined as

&nbsp;&nbsp;
\f$
\rho = \displaystyle\frac{ f(x_k) - f(x_k + d) } { m_k(0) - m_k(d) }
\f$

An iteration consists of the following steps.

<ul>
<li> Compute Newton-like direction: \f$n\f$

<li> Compute Cauchy-like direction: \f$c\f$

<li> If this is the first iteration, initialize \f$\Delta\f$ as
     follows: If \f$\|n\|_2 < \Delta_{\min}\f$, then \f$\Delta = 2
     \Delta_{\min}\f$; else, \f$\Delta = \|n\|_2\f$.

<li> Initialize \f$\rho = -1\f$

<li> While \f$\rho < \rho_{\min}\f$ and \f$\Delta > \Delta_{\min}\f$, do the following.

     <ul>
     <li> Compute the direction \f$d\f$ as follows:

          <ul>

          <li> If \f$\|n\|_2 < \Delta\f$, then take a Newton step by
               setting \f$d = n\f$

	  <li> Otherwise if \f$\|c\|_2 > \Delta\f$, then take a Cauchy
               step by setting \f$d =
               \displaystyle\frac{\Delta}{\|c\|_2} c\f$

	  <li> Otherwise, take a Dog Leg step by setting
               \f$ d = (1-\gamma) c + \gamma n \f$ where
	       \f$
	       \gamma = \displaystyle\frac
	       {-c^T a + \sqrt{ (c^Ta)^2 - (c^Tc - \Delta^2) a^Ta}}{a^Ta}
	       \f$
	       with \f$a = n-c\f$.

          </ul>

     <li> Set \f$x_{\rm new} = x + d\f$ and calculate \f$f_{\rm new}\f$

     <li> If \f$f_{\rm new} \geq f\f$, then \f$\rho = -1\f$ Otherwise
	  \f$ \rho = \displaystyle \frac {f - f_{\rm new}} {| d^T J F
	  + \frac{1}{2} (J d)^T (J d)|} \f$

     </ul>

<li> Update the solution: \f$x = x_{\rm new}\f$

<li> Update trust region:

     <ul>

     <li> If \f$\rho < \rho_{\rm s}\f$ and \f$\|n\|_2 < \Delta\f$,
          then shrink the trust region to the size of the Newton step:
          \f$\Delta = \|n\|_2\f$.

     <li> Otherwise if \f$\rho < \rho_{\rm s}\f$, then shrink the
          trust region: \f$\Delta = \max \{ \beta_{\rm s} \Delta,
          \Delta_{\min} \} \f$.

     <li> Otherwise if \f$\rho > \rho_{\rm e}\f$ and \f$\|d\|_2 =
          \Delta\f$, then expand the trust region: \f$\Delta = \min \{
          \beta_{\rm e} \Delta, \Delta_{\rm max} \} \f$.

     </ul>

</ul>

<B>Input Paramters</B>

The following parameters should be specified in the "Trust Region"
sublist based to the solver.

  - "Direction" - Sublist of the direction parameters for the %Newton
    point, passed to the NOX::Direction::Manager constructor. If this
    sublist does not exist, it is created by default. Furthermore, if
    "Method" is not specified in this sublist, it is added with a value of
    "Newton".

  - "Cauchy %Direction" - Sublist of the direction parameters for the
    Cauchy point, passed to the NOX::Direction::Manager
    constructor. If this sublist does not exist, it is created by
    default. Furthremore, if "Method" is not specified in this
    sublist, it is added with a value of "Steepest Descent" Finally,
    if the sub-sublist "Steepest Descent" does not exist, it is
    created and the parameter "Scaling Type" is added and set to
    "Quadratic".

- "Minimum Trust Region Radius" (\f$\Delta_{\min}\f$) - Minimum allowable trust region
  radius. Defaults to 1.0e-6.

- "Maximum Trust Region Radius" (\f$\Delta_{\max}\f$) - Maximum allowable trust region
  radius. Defaults to 1.0e+10.

- "Minimum Improvement Ratio" (\f$\rho_{\min}\f$) - Minimum improvement ratio to accept
  the step. Defaults to 1.0e-4.

- "Contraction Trigger Ratio" (\f$\rho_{\rm s}\f$) - If the improvement ratio is less than
  this value, then the trust region is contracted by the amount
  specified by the "Contraction Factor". Must be larger than "Minimum
  Improvement Ratio". Defaults to 0.1.

- "Contraction Factor" (\f$\beta_{\rm s}\f$) - See above. Defaults to 0.25.

- "Expansion Trigger Ratio" (\f$\rho_{\rm e}\f$) - If the
  improvement ratio is greater than this value, then the trust region
  is contracted by the amount specified by the "Expansion
  Factor". Defaults to 0.75.

- "Expansion Factor"  (\f$\beta_{\rm e}\f$) - See above. Defaults to 4.0.

- "Recovery Step" - Defaults to 1.0.

- "Use Ared/Pred Ratio Calculation" (boolean) - Defaults to false. If
  set to true, this option replaces the algorithm used to compute the
  improvement ratio, \f$ \rho \f$, as described above.  The improvement
  ratio is replaced by an "Ared/Pred" sufficient decrease criteria
  similar to that used in line search algorithms (see Eisenstat and
  Walker, SIAM Journal on Optimization V4 no. 2 (1994) pp 393-422):
  - \f$\rho = \frac{\|F(x) \| - \| F(x + d) \| }
                   {\| F(x) \| - \| F(x) + Jd \| } \f$

  - "Solver Options" - Sublist of general solver options.
     <ul>
     <li> "User Defined Pre/Post Operator" is supported.  See NOX::Parameter::PrePostOperator for more details.
     </ul>


<B>Output Paramters</B>

A sublist for output parameters called "Output" will be created and contain the following parameters:

- "Nonlinear Iterations" - Number of nonlinear iterations

- "2-Norm or Residual" - Two-norm of final residual

  \author Tammy Kolda (SNL 8950), Roger Pawlowski (SNL 9233)
*/

class TrustRegionBased : public Generic {

public:

  /*!
    \brief Constructor

    See reset() for description.
  */
  TrustRegionBased(const Teuchos::RCP<NOX::Abstract::Group>& grp,
		   const Teuchos::RCP<NOX::StatusTest::Generic>& tests,
		   const Teuchos::RCP<Teuchos::ParameterList>& params);

  //! Destructor
  virtual ~TrustRegionBased();

  virtual void reset(const NOX::Abstract::Vector& initialGuess,
		     const Teuchos::RCP<NOX::StatusTest::Generic>& tests);
  virtual void reset(const NOX::Abstract::Vector& initialGuess);
  virtual NOX::StatusTest::StatusType getStatus();
  virtual NOX::StatusTest::StatusType step();
  virtual NOX::StatusTest::StatusType solve();
  virtual const NOX::Abstract::Group& getSolutionGroup() const;
  virtual const NOX::Abstract::Group& getPreviousSolutionGroup() const;
  virtual int getNumIterations() const;
  virtual const Teuchos::ParameterList& getList() const;

  inline virtual Teuchos::RCP< const NOX::Abstract::Group > getSolutionGroupPtr() const {return solnPtr;};
  inline virtual Teuchos::RCP< const NOX::Abstract::Group > getPreviousSolutionGroupPtr() const {return oldSolnPtr;};
  inline virtual Teuchos::RCP< const Teuchos::ParameterList > getListPtr() const {return paramsPtr;};

protected:

  //! Print out initialization information and calcuation the RHS.
  virtual void init();

  //! Print and error message and throw and error
  virtual void invalid(const std::string& param, double value) const;

  //! Prints the current iteration information.
  virtual void printUpdate();

protected:

  //! Pointer to the global data object.
  Teuchos::RCP<NOX::GlobalData> globalDataPtr;

  //! Printing Utils
  Teuchos::RCP<NOX::Utils> utilsPtr;

  //! Current solution.
  Teuchos::RCP<NOX::Abstract::Group> solnPtr;

  //! Previous solution pointer.
  /*! We have both a pointer and a reference because we need to create
    a DERIVED object and then want to have a reference to it. */
  Teuchos::RCP<NOX::Abstract::Group> oldSolnPtr;

  //! Current search direction.pointer.
  /*! We have both a pointer and a reference because we need to create
    a DERIVED object and then want to have a reference to it. */
  Teuchos::RCP<NOX::Abstract::Vector> newtonVecPtr;

  //! Current search direction.pointer.
  /*! We have both a pointer and a reference because we need to create
    a DERIVED object and then want to have a reference to it. */
  Teuchos::RCP<NOX::Abstract::Vector> cauchyVecPtr;

  //! Extra vector used in computations
  /*! We have both a pointer and a reference because we need to create
    a DERIVED object and then want to have a reference to it. */
  Teuchos::RCP<NOX::Abstract::Vector> aVecPtr;

  //! Extra vector used in computations
  /*! We have both a pointer and a reference because we need to create
    a DERIVED object and then want to have a reference to it. */
  Teuchos::RCP<NOX::Abstract::Vector> bVecPtr;

  //! Stopping test.
  Teuchos::RCP<NOX::StatusTest::Generic> testPtr;

  //! Type of check to use for status tests.  See NOX::StatusTest for more details.
  NOX::StatusTest::CheckType checkType;

  //! Input parameters.
  Teuchos::RCP<Teuchos::ParameterList> paramsPtr;

  //! %Newton %Search %Direction.
  Teuchos::RCP<NOX::Direction::Generic> newtonPtr;

  //! Cauchy %Search %Direction.
  Teuchos::RCP<NOX::Direction::Generic> cauchyPtr;

  //! Radius of the trust region
  double radius;

  //! Minimum improvement ratio to accept step
  double minRatio;

  //! Initial trust region radius
  double initRadius;

  //! Minimum trust region radius
  double minRadius;

  //! Maximum trust region radius
  double maxRadius;

  //! ratio < alpha triggers contraction
  double contractTriggerRatio;

  //! ratio > beta triggers expansion
  double expandTriggerRatio;

  //! Expansion factor
  double expandFactor;

  //! Constraction factor
  double contractFactor;

  //! Take a step of this length in the Newton direction if the
  //! trust-region search fails
  double recoveryStep;

  //! Value of \f$ f \f$ at current solution
  double newF;
  //! Value of \f$ f \f$ at previous solution
  double oldF;

  //! norm(xnew - xold)
  double dx;

  //! Number of nonlinear iterations.
  int nIter;

  //! %Status of nonlinear solver.
  NOX::StatusTest::StatusType status;

  //! Enumerated list for each direction that may be required in the Trust region computation.
  enum StepType
  {
    //! Use the Newton direction
    Newton,
    //! Use the Cauchy direction
    Cauchy,
    //! Use the doglog direction
    Dogleg
  };

  //! Type of step to be taken.
  StepType stepType;

  //! Stores a user supplied merit function if supplied in the parameter list.
  Teuchos::RCP<NOX::MeritFunction::Generic> meritFuncPtr;

  //! If set to true, the minimum improvement ratio condition uses an Ared/Pred approach.
  bool useAredPredRatio;

  //! Pointer to a user defined NOX::Abstract::PrePostOperator object.
  NOX::Solver::PrePostOperator prePostOperator;

};
} // namespace Solver
} // namespace NOX

#endif