libtrilinos-rol-dev 12.10.1-3 / usr / include / trilinos / ROL_BoundConstraint.hpp

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#ifndef ROL_BOUND_CONSTRAINT_H
#define ROL_BOUND_CONSTRAINT_H

#include "ROL_Vector.hpp"
#include "ROL_Types.hpp"
#include <iostream>

/** @ingroup func_group
    \class ROL::BoundConstraint
    \brief Provides the interface to apply upper and lower bound constraints.

    ROL's bound constraint class is to designed to handle point wise bound 
    constraints on optimization variables.  That is, let \f$\mathcal{X}\f$ 
    be a Banach space of functions from \f$\Xi\f$ into \f$\mathbb{R}\f$ 
    (for example, \f$\Xi\subset\mathbb{R}^d\f$ for some positive integer \f$d\f$
    and \f$\mathcal{X}=L^2(\Xi)\f$ or \f$\Xi = \{1,\ldots,n\}\f$ and 
    \f$\mathcal{X}=\mathbb{R}^n\f$).  For any \f$x\in\mathcal{X}\f$, we consider 
    bounds of the form 
    \f[
        a(\xi) \le x(\xi) \le b(\xi) \quad \text{for almost every }\xi\in\Xi.
    \f] 
    Here, \f$a(\xi)\le b(\xi)\f$ for almost every \f$\xi\in\Xi\f$ and \f$a,b\in \mathcal{X}\f$.
*/


namespace ROL {

template <class Real>
class BoundConstraint {
private:
  int dim_;

  const Teuchos::RCP<Vector<Real> > x_lo_;
  const Teuchos::RCP<Vector<Real> > x_up_;
  const Real scale_;  

  Teuchos::RCP<Vector<Real> > mask_;

  bool activated_; ///< Flag that determines whether or not the constraints are being used.
  Real min_diff_;

  Elementwise::ReductionMin<Real> minimum_;

  class Active : public Elementwise::BinaryFunction<Real> {
    public:
    Active(Real offset) : offset_(offset) {}
    Real apply( const Real &x, const Real &y ) const {
      return ((y <= offset_) ? 0 : x);
    }
    private:
    Real offset_;
  };

  class UpperBinding : public Elementwise::BinaryFunction<Real> {
    public:
    UpperBinding(Real offset) : offset_(offset) {}
    Real apply( const Real &x, const Real &y ) const {
      return ((y < 0 && x <= offset_) ? 0 : 1);
    }
    private:
    Real offset_;
  };

  class LowerBinding : public Elementwise::BinaryFunction<Real> {
    public:
    LowerBinding(Real offset) : offset_(offset) {}
    Real apply( const Real &x, const Real &y ) const {
      return ((y > 0 && x <= offset_) ? 0 : 1);
    }
    private:
    Real offset_;
  };

  class PruneBinding : public Elementwise::BinaryFunction<Real> {
    public:
      Real apply( const Real &x, const Real &y ) const {
        return ((y == 1) ? x : 0);
      }
  } prune_;

public:

  virtual ~BoundConstraint() {}

  BoundConstraint(void)
    : x_lo_(Teuchos::null), x_up_(Teuchos::null), scale_(1),
      mask_(Teuchos::null), activated_(false), min_diff_(0) {}

  BoundConstraint( const Vector<Real> &x ) : x_lo_(x.clone()), 
      x_up_(x.clone()), scale_(1),
      mask_(Teuchos::null), activated_(false), min_diff_(0) {
    x_lo_->applyUnary(Elementwise::Fill<Real>(ROL_NINF<Real>()));
    x_up_->applyUnary(Elementwise::Fill<Real>(ROL_INF<Real>()));

  }
  /** \brief Default constructor.

      The default constructor automatically turns the constraints on.
  */
  BoundConstraint(const Teuchos::RCP<Vector<Real> > &x_lo,
                  const Teuchos::RCP<Vector<Real> > &x_up,
                  const Real scale = 1)
    : x_lo_(x_lo), x_up_(x_up), scale_(scale), activated_(true) {
    Real half(0.5), one(1);
    mask_ = x_lo_->clone();

    // Compute difference between upper and lower bounds
    mask_->set(*x_up_);
    mask_->axpy(-one,*x_lo_);

    // Compute minimum difference
    min_diff_ = mask_->reduce(minimum_);
    min_diff_ *= half;

  }

  /** \brief Update bounds.

      The update function allows the user to update the bounds at each new iterations.
          @param[in]      x      is the optimization variable.
          @param[in]      flag   is set to true if control is changed.
          @param[in]      iter   is the outer algorithm iterations count.
  */
  virtual void update( const Vector<Real> &x, bool flag = true, int iter = -1 ) {}

  /** \brief Project optimization variables onto the bounds.

      This function implements the projection of \f$x\f$ onto the bounds, i.e.,
      \f[
         (P_{[a,b]}(x))(\xi) = \min\{b(\xi),\max\{a(\xi),x(\xi)\}\} \quad \text{for almost every }\xi\in\Xi.
      \f]
       @param[in,out]      x is the optimization variable.
  */
  virtual void project( Vector<Real> &x ) {

    struct Lesser : public Elementwise::BinaryFunction<Real> {
      Real apply(const Real &xc, const Real &yc) const { return xc<yc ? xc : yc; }
    } lesser;

    struct Greater : public Elementwise::BinaryFunction<Real> {
      Real apply(const Real &xc, const Real &yc) const { return xc>yc ? xc : yc; }
    } greater;

    x.applyBinary(lesser, *x_up_); // Set x to the elementwise minimum of x and x_up_
    x.applyBinary(greater,*x_lo_); // Set x to the elementwise maximum of x and x_lo_

  }

  /** \brief Set variables to zero if they correspond to the upper \f$\epsilon\f$-active set.

      This function sets \f$v(\xi)=0\f$ if \f$\xi\in\mathcal{A}^+_\epsilon(x)\f$.  Here,
      the upper \f$\epsilon\f$-active set is defined as
      \f[
         \mathcal{A}^+_\epsilon(x) = \{\,\xi\in\Xi\,:\,x(\xi) = b(\xi)-\epsilon\,\}.
      \f]
      @param[out]      v   is the variable to be pruned.
      @param[in]       x   is the current optimization variable.
      @param[in]       eps is the active-set tolerance \f$\epsilon\f$.
  */
  virtual void pruneUpperActive( Vector<Real> &v, const Vector<Real> &x, Real eps = 0 ) {

    Real one(1), epsn(std::min(scale_*eps,min_diff_));

    mask_->set(*x_up_);
    mask_->axpy(-one,x);

    Active op(epsn);
    v.applyBinary(op,*mask_);

  }

  /** \brief Set variables to zero if they correspond to the upper \f$\epsilon\f$-binding set.

      This function sets \f$v(\xi)=0\f$ if \f$\xi\in\mathcal{B}^+_\epsilon(x)\f$.  Here,
      the upper \f$\epsilon\f$-binding set is defined as
      \f[
         \mathcal{B}^+_\epsilon(x) = \{\,\xi\in\Xi\,:\,x(\xi) = b(\xi)-\epsilon,\;
                g(\xi) < 0 \,\}.
      \f]
      @param[out]      v   is the variable to be pruned.
      @param[in]       g   is the negative search direction.
      @param[in]       x   is the current optimization variable.
      @param[in]       eps is the active-set tolerance \f$\epsilon\f$.
  */
  virtual void pruneUpperActive( Vector<Real> &v, const Vector<Real> &g, const Vector<Real> &x, Real eps = 0 ) {

    Real one(1), epsn(std::min(scale_*eps,min_diff_));

    mask_->set(*x_up_);
    mask_->axpy(-one,x);
    
    UpperBinding op(epsn);
    mask_->applyBinary(op,g);

    v.applyBinary(prune_,*mask_);

  }

  /** \brief Set variables to zero if they correspond to the lower \f$\epsilon\f$-active set.

      This function sets \f$v(\xi)=0\f$ if \f$\xi\in\mathcal{A}^-_\epsilon(x)\f$.  Here,
      the lower \f$\epsilon\f$-active set is defined as
      \f[
         \mathcal{A}^-_\epsilon(x) = \{\,\xi\in\Xi\,:\,x(\xi) = a(\xi)+\epsilon\,\}.
      \f]
      @param[out]      v   is the variable to be pruned.
      @param[in]       x   is the current optimization variable.
      @param[in]       eps is the active-set tolerance \f$\epsilon\f$.
  */
  virtual void pruneLowerActive( Vector<Real> &v, const Vector<Real> &x, Real eps = 0 ) {

    Real one(1), epsn(std::min(scale_*eps,min_diff_));

    mask_->set(x);
    mask_->axpy(-one,*x_lo_);

    Active op(epsn);
    v.applyBinary(op,*mask_);

  }

  /** \brief Set variables to zero if they correspond to the lower \f$\epsilon\f$-binding set.

      This function sets \f$v(\xi)=0\f$ if \f$\xi\in\mathcal{B}^-_\epsilon(x)\f$.  Here,
      the lower \f$\epsilon\f$-binding set is defined as
      \f[
         \mathcal{B}^-_\epsilon(x) = \{\,\xi\in\Xi\,:\,x(\xi) = a(\xi)+\epsilon,\;
                g(\xi) > 0 \,\}.
      \f]
      @param[out]      v   is the variable to be pruned.
      @param[in]       g   is the negative search direction.
      @param[in]       x   is the current optimization variable.
      @param[in]       eps is the active-set tolerance \f$\epsilon\f$.
  */
  virtual void pruneLowerActive( Vector<Real> &v, const Vector<Real> &g, const Vector<Real> &x, Real eps = 0 ) {

    Real one(1), epsn(std::min(scale_*eps,min_diff_));

    mask_->set(x);
    mask_->axpy(-one,*x_lo_);

    LowerBinding op(epsn);
    mask_->applyBinary(op,g);

    v.applyBinary(prune_,*mask_);

  }

  /** \brief Return the ref count pointer to the lower bound vector */
  virtual const Teuchos::RCP<const Vector<Real> > getLowerVectorRCP( void ) const {
    return x_lo_;
  }

  /** \brief Return the ref count pointer to the upper bound vector */
  virtual const Teuchos::RCP<const Vector<Real> > getUpperVectorRCP( void ) const {
    return x_up_;
  }

   /** \brief Return the ref count pointer to the lower bound vector */
  virtual  const Teuchos::RCP<Vector<Real> > getLowerVectorRCP( void ) {
    return x_lo_;
  }

  /** \brief Return the ref count pointer to the upper bound vector */
  virtual const Teuchos::RCP<Vector<Real> > getUpperVectorRCP( void ) {
    return x_up_;
  }

    

  /** \brief Set the input vector to the upper bound.

      This function sets the input vector \f$u\f$ to the upper bound \f$b\f$.
      @param[out]    u   is the vector to be set to the upper bound.
  */ 
  virtual void setVectorToUpperBound( Vector<Real> &u ) {
    if( x_up_ == Teuchos::null ) {
      u.applyUnary(Elementwise::Fill<Real>(ROL_INF<Real>()));
    }
    else {
      u.set(*x_up_);
    }
  }

  /** \brief Set the input vector to the lower bound.

      This function sets the input vector \f$l\f$ to the lower bound \f$a\f$.
      @param[out]    l   is the vector to be set to the lower bound.
  */ 
  virtual void setVectorToLowerBound( Vector<Real> &l ) {
    if( x_lo_ == Teuchos::null ) {
      l.applyUnary(Elementwise::Fill<Real>(ROL_NINF<Real>()));
    }
    else {
      l.set(*x_lo_);
    }
  }

  /** \brief Set variables to zero if they correspond to the \f$\epsilon\f$-active set.

      This function sets \f$v(\xi)=0\f$ if \f$\xi\in\mathcal{A}_\epsilon(x)\f$.  Here,
      the \f$\epsilon\f$-active set is defined as
      \f[
         \mathcal{A}_\epsilon(x) = \mathcal{A}^+_\epsilon(x)\cap\mathcal{A}^-_\epsilon(x).
      \f]
      @param[out]      v   is the variable to be pruned.
      @param[in]       x   is the current optimization variable.
      @param[in]       eps is the active-set tolerance \f$\epsilon\f$.
  */
  virtual void pruneActive( Vector<Real> &v, const Vector<Real> &x, Real eps = 0 ) {
    pruneUpperActive(v,x,eps);
    pruneLowerActive(v,x,eps);
  }

  /** \brief Set variables to zero if they correspond to the \f$\epsilon\f$-binding set.
  
      This function sets \f$v(\xi)=0\f$ if \f$\xi\in\mathcal{B}_\epsilon(x)\f$.  Here, 
      the \f$\epsilon\f$-binding set is defined as 
      \f[
         \mathcal{B}^+_\epsilon(x) = \mathcal{B}^+_\epsilon(x)\cap\mathcal{B}^-_\epsilon(x).
      \f]
      @param[out]      v   is the variable to be pruned.
      @param[in]       g   is the negative search direction.
      @param[in]       x   is the current optimization variable.
      @param[in]       eps is the active-set tolerance \f$\epsilon\f$.
  */
  virtual void pruneActive( Vector<Real> &v, const Vector<Real> &g, const Vector<Real> &x, Real eps = 0 ) {
    pruneUpperActive(v,g,x,eps);
    pruneLowerActive(v,g,x,eps);
  }

  /** \brief Check if the vector, v, is feasible.

      This function returns true if \f$v = P_{[a,b]}(v)\f$.
      @param[in]    v   is the vector to be checked.
  */
  virtual bool isFeasible( const Vector<Real> &v ) { 
    bool flag = true;
    Real one(1);
    if ( activated_ ) {
      mask_->set(*x_up_);
      mask_->axpy(-one,v);
      Real uminusv = mask_->reduce(minimum_);

      mask_->set(v);
      mask_->axpy(-one,*x_lo_);
      Real vminusl = mask_->reduce(minimum_);

      flag = (((uminusv < 0) || (vminusl<0)) ? false : true);
    }
    return flag;
  }

  /** \brief Turn on bounds.
   
      This function turns the bounds on. 
  */
  void activate(void)    { activated_ = true;  }

  /** \brief Turn off bounds.

      This function turns the bounds off.
  */
  void deactivate(void)  { activated_ = false; }

  /** \brief Check if bounds are on.

      This function returns true if the bounds are turned on.
  */
  bool isActivated(void) { return activated_;  }

  /** \brief Set variables to zero if they correspond to the \f$\epsilon\f$-inactive set.
  
      This function sets \f$v(\xi)=0\f$ if \f$\xi\in\Xi\setminus\mathcal{A}_\epsilon(x)\f$.  Here, 
      @param[out]      v   is the variable to be pruned.
      @param[in]       x   is the current optimization variable.
      @param[in]       eps is the active-set tolerance \f$\epsilon\f$.
  */
  void pruneInactive( Vector<Real> &v, const Vector<Real> &x, Real eps = 0 ) { 
    Real one(1);
    Teuchos::RCP<Vector<Real> > tmp = v.clone(); 
    tmp->set(v);
    pruneActive(*tmp,x,eps);
    v.axpy(-one,*tmp);
  }
  void pruneLowerInactive( Vector<Real> &v, const Vector<Real> &x, Real eps = 0 ) {
    Real one(1);
    Teuchos::RCP<Vector<Real> > tmp = v.clone(); 
    tmp->set(v);
    pruneLowerActive(*tmp,x,eps);
    v.axpy(-one,*tmp);
  }
  void pruneUpperInactive( Vector<Real> &v, const Vector<Real> &x, Real eps = 0 ) { 
    Real one(1);
    Teuchos::RCP<Vector<Real> > tmp = v.clone(); 
    tmp->set(v);
    pruneUpperActive(*tmp,x,eps);
    v.axpy(-one,*tmp);
  }


  /** \brief Set variables to zero if they correspond to the \f$\epsilon\f$-nonbinding set.
  
      This function sets \f$v(\xi)=0\f$ if \f$\xi\in\Xi\setminus\mathcal{B}_\epsilon(x)\f$.  
      @param[out]      v   is the variable to be pruned.
      @param[in]       x   is the current optimization variable.
      @param[in]       g   is the negative search direction.
      @param[in]       eps is the active-set tolerance \f$\epsilon\f$.
  */
  void pruneInactive( Vector<Real> &v, const Vector<Real> &g, const Vector<Real> &x, Real eps = 0 ) { 
    Real one(1);
    Teuchos::RCP<Vector<Real> > tmp = v.clone(); 
    tmp->set(v);
    pruneActive(*tmp,g,x,eps);
    v.axpy(-one,*tmp);
  }
  void pruneLowerInactive( Vector<Real> &v, const Vector<Real> &g, const Vector<Real> &x, Real eps = 0 ) { 
    Real one(1);
    Teuchos::RCP<Vector<Real> > tmp = v.clone(); 
    tmp->set(v);
    pruneLowerActive(*tmp,g,x,eps);
    v.axpy(-one,*tmp);
  }
  void pruneUpperInactive( Vector<Real> &v, const Vector<Real> &g, const Vector<Real> &x, Real eps = 0 ) { 
    Real one(1);
    Teuchos::RCP<Vector<Real> > tmp = v.clone(); 
    tmp->set(v);
    pruneUpperActive(*tmp,g,x,eps);
    v.axpy(-one,*tmp);
  }
 
  /** \brief Compute projected gradient.

      This function projects the gradient \f$g\f$ onto the tangent cone.
           @param[in,out]    g  is the gradient of the objective function at x.
           @param[in]        x  is the optimization variable
  */
  void computeProjectedGradient( Vector<Real> &g, const Vector<Real> &x ) {
    Teuchos::RCP<Vector<Real> > tmp = g.clone();
    tmp->set(g);
    pruneActive(g,*tmp,x);
  }
 
  /** \brief Compute projected step.

      This function computes the projected step \f$P_{[a,b]}(x+v) - x\f$.
      @param[in,out]         v  is the step variable.
      @param[in]             x is the optimization variable.
  */
  void computeProjectedStep( Vector<Real> &v, const Vector<Real> &x ) { 
    Real one(1);
    v.plus(x);
    project(v);
    v.axpy(-one,x);
  }

}; // class BoundConstraint

} // namespace ROL

#endif