C++ BoundConstraint::project方法代码示例

 void updateIterate(Vector<Real> &xnew, const Vector<Real> &x, const Vector<Real> &s, Real alpha,
                    BoundConstraint<Real> &con ) {
   xnew.set(x);
   xnew.axpy(alpha,s);
   if ( con.isActivated() ) {
     con.project(xnew);
   }
 }

  /** \brief Compute the gradient-based criticality measure.

             The criticality measure is 
             \f$\|x_k - P_{[a,b]}(x_k-\nabla f(x_k))\|_{\mathcal{X}}\f$.
             Here, \f$P_{[a,b]}\f$ denotes the projection onto the
             bound constraints.
 
             @param[in]    x     is the current iteration
             @param[in]    obj   is the objective function
             @param[in]    con   are the bound constraints
             @param[in]    tol   is a tolerance for inexact evaluations of the objective function
  */ 
  Real computeCriticalityMeasure(Vector<Real> &x, Objective<Real> &obj, BoundConstraint<Real> &con, Real tol) {
    Teuchos::RCP<StepState<Real> > step_state = Step<Real>::getState();
    obj.gradient(*(step_state->gradientVec),x,tol);
    xtmp_->set(x);
    xtmp_->axpy(-1.0,(step_state->gradientVec)->dual());
    con.project(*xtmp_);
    xtmp_->axpy(-1.0,x);
    return xtmp_->norm();
  }

  void update( Vector<Real> &x, const Vector<Real> &s,
               Objective<Real> &obj, BoundConstraint<Real> &bnd,
               AlgorithmState<Real> &algo_state ) {
    Real tol = std::sqrt(ROL_EPSILON<Real>()), one(1);
    Teuchos::RCP<StepState<Real> > step_state = Step<Real>::getState();

    // Update iterate and store previous step
    algo_state.iter++;
    d_->set(x);
    x.plus(s);
    bnd.project(x);
    (step_state->descentVec)->set(x);
    (step_state->descentVec)->axpy(-one,*d_);
    algo_state.snorm = s.norm();

    // Compute new gradient
    gp_->set(*(step_state->gradientVec));
    obj.update(x,true,algo_state.iter);
    if ( computeObj_ ) {
      algo_state.value = obj.value(x,tol);
      algo_state.nfval++;
    }
    obj.gradient(*(step_state->gradientVec),x,tol);
    algo_state.ngrad++;

    // Update Secant Information
    secant_->updateStorage(x,*(step_state->gradientVec),*gp_,s,algo_state.snorm,algo_state.iter+1);

    // Update algorithm state
    (algo_state.iterateVec)->set(x);
    if ( useProjectedGrad_ ) {
      gp_->set(*(step_state->gradientVec));
      bnd.computeProjectedGradient( *gp_, x );
      algo_state.gnorm = gp_->norm();
    }
    else {
      d_->set(x);
      d_->axpy(-one,(step_state->gradientVec)->dual());
      bnd.project(*d_);
      d_->axpy(-one,x);
      algo_state.gnorm = d_->norm();
    }
  }

  /** \brief Update step, if successful.

      Given a trial step, \f$s_k\f$, this function updates \f$x_{k+1}=x_k+s_k\f$. 
      This function also updates the secant approximation.

      @param[in,out]   x          is the updated iterate
      @param[in]       s          is the computed trial step
      @param[in]       obj        is the objective function
      @param[in]       con        are the bound constraints
      @param[in]       algo_state contains the current state of the algorithm
  */
  void update( Vector<Real> &x, const Vector<Real> &s, Objective<Real> &obj, BoundConstraint<Real> &con,
               AlgorithmState<Real> &algo_state ) {
    Real tol = std::sqrt(ROL_EPSILON);
    Teuchos::RCP<StepState<Real> > step_state = Step<Real>::getState();

    

    // Update iterate
    algo_state.iter++;
    x.axpy(1.0, s);
    // Compute new gradient
    if ( edesc_ == DESCENT_SECANT || 
        (edesc_ == DESCENT_NEWTONKRYLOV && useSecantPrecond_) ) {
      gp_->set(*(step_state->gradientVec));
    }
    obj.gradient(*(step_state->gradientVec),x,tol);
    algo_state.ngrad++;

    // Update Secant Information
    if ( edesc_ == DESCENT_SECANT || 
        (edesc_ == DESCENT_NEWTONKRYLOV && useSecantPrecond_) ) {
      secant_->update(*(step_state->gradientVec),*gp_,s,algo_state.snorm,algo_state.iter+1);
    }

    // Update algorithm state
    (algo_state.iterateVec)->set(x);
    if ( con.isActivated() ) {
      if ( useProjectedGrad_ ) {
        gp_->set(*(step_state->gradientVec));
        con.computeProjectedGradient( *gp_, x );
        algo_state.gnorm = gp_->norm();
      }
      else {
        d_->set(x);
        d_->axpy(-1.0,(step_state->gradientVec)->dual());
        con.project(*d_);
        d_->axpy(-1.0,x);
        algo_state.gnorm = d_->norm();
      }
    }
    else {
      algo_state.gnorm = (step_state->gradientVec)->norm();
    }
  }

  /** \brief Initialize step.  

             This includes projecting the initial guess onto the constraints, 
             computing the initial objective function value and gradient, 
             and initializing the dual variables.

             @param[in,out]    x           is the initial guess 
             @param[in]        obj         is the objective function
             @param[in]        con         are the bound constraints
             @param[in]        algo_state  is the current state of the algorithm
  */
  void initialize( Vector<Real> &x, const Vector<Real> &s, const Vector<Real> &g, 
                   Objective<Real> &obj, BoundConstraint<Real> &con, 
                   AlgorithmState<Real> &algo_state ) {
    Teuchos::RCP<StepState<Real> > step_state = Step<Real>::getState();
    // Initialize state descent direction and gradient storage
    step_state->descentVec  = s.clone();
    step_state->gradientVec = g.clone();
    step_state->searchSize  = 0.0;
    // Initialize additional storage
    xlam_ = x.clone(); 
    x0_   = x.clone();
    xbnd_ = x.clone();
    As_   = s.clone(); 
    xtmp_ = x.clone(); 
    res_  = g.clone();
    Ag_   = g.clone(); 
    rtmp_ = g.clone(); 
    gtmp_ = g.clone(); 
    // Project x onto constraint set
    con.project(x);
    // Update objective function, get value, and get gradient
    Real tol = std::sqrt(ROL_EPSILON);
    obj.update(x,true,algo_state.iter);
    algo_state.value = obj.value(x,tol);
    algo_state.nfval++;
    algo_state.gnorm = computeCriticalityMeasure(x,obj,con,tol);
    algo_state.ngrad++;
    // Initialize dual variable
    lambda_ = s.clone(); 
    lambda_->set((step_state->gradientVec)->dual());
    lambda_->scale(-1.0);
    //con.setVectorToLowerBound(*lambda_);
    // Initialize Hessian and preconditioner
    Teuchos::RCP<Objective<Real> > obj_ptr = Teuchos::rcp(&obj, false);
    Teuchos::RCP<BoundConstraint<Real> > con_ptr = Teuchos::rcp(&con, false);
    hessian_ = Teuchos::rcp( 
      new PrimalDualHessian<Real>(secant_,obj_ptr,con_ptr,algo_state.iterateVec,xlam_,useSecantHessVec_) );
    precond_ = Teuchos::rcp( 
      new PrimalDualPreconditioner<Real>(secant_,obj_ptr,con_ptr,algo_state.iterateVec,xlam_,
                                         useSecantPrecond_) );
  }

 Real GradDotStep(const Vector<Real> &g, const Vector<Real> &s,
                  const Vector<Real> &x,
                  BoundConstraint<Real> &bnd, Real eps = 0) {
   Real gs(0), one(1);
   if (!bnd.isActivated()) {
     gs = s.dot(g.dual());
   }
   else {
     d_->set(s);
     bnd.pruneActive(*d_,g,x,eps);
     gs = d_->dot(g.dual());
     d_->set(x);
     d_->axpy(-one,g.dual());
     bnd.project(*d_);
     d_->scale(-one);
     d_->plus(x);
     bnd.pruneInactive(*d_,g,x,eps);
     gs -= d_->dot(g.dual());
   }
   return gs;
 }

  /** \brief Compute step.

      Computes a trial step, \f$s_k\f$ as defined by the enum EDescent.  Once the 
      trial step is determined, this function determines an approximate minimizer 
      of the 1D function \f$\phi_k(t) = f(x_k+ts_k)\f$.  This approximate 
      minimizer must satisfy sufficient decrease and curvature conditions.

      @param[out]      s          is the computed trial step
      @param[in]       x          is the current iterate
      @param[in]       obj        is the objective function
      @param[in]       con        are the bound constraints
      @param[in]       algo_state contains the current state of the algorithm
  */
  void compute( Vector<Real> &s, const Vector<Real> &x, Objective<Real> &obj, BoundConstraint<Real> &con, 
                AlgorithmState<Real> &algo_state ) {
    Teuchos::RCP<StepState<Real> > step_state = Step<Real>::getState();

    Real tol = std::sqrt(ROL_EPSILON);

    // Set active set parameter
    Real eps = 0.0;
    if ( con.isActivated() ) {
      eps = algo_state.gnorm;
    }
    lineSearch_->setData(eps);
    if ( hessian_ != Teuchos::null ) {
      hessian_->setData(eps);
    }
    if ( precond_ != Teuchos::null ) {
      precond_->setData(eps);
    }

    // Compute step s
    switch(edesc_) {
      case DESCENT_NEWTONKRYLOV:
        flagKrylov_ = 0;
        krylov_->run(s,*hessian_,*(step_state->gradientVec),*precond_,iterKrylov_,flagKrylov_);
        break;
      case DESCENT_NEWTON:
      case DESCENT_SECANT:
        hessian_->applyInverse(s,*(step_state->gradientVec),tol);
        break;
      case DESCENT_NONLINEARCG:
        nlcg_->run(s,*(step_state->gradientVec),x,obj);
        break;
      case DESCENT_STEEPEST:
        s.set(step_state->gradientVec->dual());
        break;
      default: break;
    }

    // Compute g.dot(s)
    Real gs = 0.0;
    if ( !con.isActivated() ) {
      gs = -s.dot((step_state->gradientVec)->dual());
    }
    else {
      if ( edesc_ == DESCENT_STEEPEST ) {
        d_->set(x);
        d_->axpy(-1.0,s);
        con.project(*d_);
        d_->scale(-1.0);
        d_->plus(x);
        //d->set(s);
        //con.pruneActive(*d,s,x,eps);
        //con.pruneActive(*d,*(step_state->gradientVec),x,eps);
        gs = -d_->dot((step_state->gradientVec)->dual());
      }
      else {
        d_->set(s);
        con.pruneActive(*d_,*(step_state->gradientVec),x,eps);
        gs = -d_->dot((step_state->gradientVec)->dual());
        d_->set(x);
        d_->axpy(-1.0,(step_state->gradientVec)->dual());
        con.project(*d_);
        d_->scale(-1.0);
        d_->plus(x);
        con.pruneInactive(*d_,*(step_state->gradientVec),x,eps);
        gs -= d_->dot((step_state->gradientVec)->dual());
      }
    }

    // Check if s is a descent direction i.e., g.dot(s) < 0
    if ( gs >= 0.0 || (flagKrylov_ == 2 && iterKrylov_ <= 1) ) {
      s.set((step_state->gradientVec)->dual());
      if ( con.isActivated() ) {
        d_->set(s);
        con.pruneActive(*d_,s,x);
        gs = -d_->dot((step_state->gradientVec)->dual());
      }
      else {
        gs = -s.dot((step_state->gradientVec)->dual());
      }
    }
    s.scale(-1.0);

    // Perform line search
    Real fnew  = algo_state.value;
    ls_nfval_ = 0;
    ls_ngrad_ = 0;
//.........这里部分代码省略.........

//.........这里部分代码省略.........
      xlam_->set(*x0_);                          // xlam = x0
      xlam_->axpy(scale_,*(lambda_));            // xlam = x0 + c*lambda
      /********************************************************************/
      // PROJECT x ONTO PRIMAL DUAL FEASIBLE SET
      /********************************************************************/
      As_->zero();                               // As   = 0
   
      con.setVectorToUpperBound(*xbnd_);         // xbnd = u        
      xbnd_->axpy(-1.0,x);                       // xbnd = u - x    
      xtmp_->set(*xbnd_);                        // tmp  = u - x    
      con.pruneUpperActive(*xtmp_,*xlam_,neps_); // tmp  = I(u - x) 
      xbnd_->axpy(-1.0,*xtmp_);                  // xbnd = A(u - x)  
      As_->plus(*xbnd_);                         // As  += A(u - x)

      con.setVectorToLowerBound(*xbnd_);         // xbnd = l
      xbnd_->axpy(-1.0,x);                       // xbnd = l - x
      xtmp_->set(*xbnd_);                        // tmp  = l - x
      con.pruneLowerActive(*xtmp_,*xlam_,neps_); // tmp  = I(l - x)
      xbnd_->axpy(-1.0,*xtmp_);                  // xbnd = A(l - x)
      As_->plus(*xbnd_);                         // As  += A(l - x)
      /********************************************************************/
      // APPLY HESSIAN TO ACTIVE COMPONENTS OF s AND REMOVE INACTIVE 
      /********************************************************************/
      itol_ = std::sqrt(ROL_EPSILON);
      if ( useSecantHessVec_ && secant_ != Teuchos::null ) {        // IHAs = H*As
        secant_->applyB(*gtmp_,*As_,x);
      }
      else {
        obj.hessVec(*gtmp_,*As_,x,itol_);
      }
      con.pruneActive(*gtmp_,*xlam_,neps_);     // IHAs = I(H*As)
      /********************************************************************/
      // SEPARATE ACTIVE AND INACTIVE COMPONENTS OF THE GRADIENT
      /********************************************************************/
      rtmp_->set(*(step_state->gradientVec));    // Inactive components
      con.pruneActive(*rtmp_,*xlam_,neps_);

      Ag_->set(*(step_state->gradientVec));     // Active components
      Ag_->axpy(-1.0,*rtmp_);
      /********************************************************************/
      // SOLVE REDUCED NEWTON SYSTEM 
      /********************************************************************/
      rtmp_->plus(*gtmp_);
      rtmp_->scale(-1.0);                        // rhs = -Ig - I(H*As)
      s.zero();
      if ( rtmp_->norm() > 0.0 ) {             
        //solve(s,*rtmp_,*xlam_,x,obj,con);   // Call conjugate residuals
        krylov_->run(s,*hessian_,*rtmp_,*precond_,iterCR_,flagCR_);
        con.pruneActive(s,*xlam_,neps_);        // s <- Is
      }
      s.plus(*As_);                             // s = Is + As
      /********************************************************************/
      // UPDATE MULTIPLIER 
      /********************************************************************/
      if ( useSecantHessVec_ && secant_ != Teuchos::null ) {
        secant_->applyB(*rtmp_,s,x);
      }
      else {
        obj.hessVec(*rtmp_,s,x,itol_);
      }
      gtmp_->set(*rtmp_);
      con.pruneActive(*gtmp_,*xlam_,neps_);
      lambda_->set(*rtmp_);
      lambda_->axpy(-1.0,*gtmp_);
      lambda_->plus(*Ag_);
      lambda_->scale(-1.0);
      /********************************************************************/
      // UPDATE STEP 
      /********************************************************************/
      x0_->set(x);
      x0_->plus(s);
      res_->set(*(step_state->gradientVec));
      res_->plus(*rtmp_);
      // Compute criticality measure  
      xtmp_->set(*x0_);
      xtmp_->axpy(-1.0,res_->dual());
      con.project(*xtmp_);
      xtmp_->axpy(-1.0,*x0_);
//      std::cout << s.norm()               << "  " 
//                << tmp->norm()            << "  " 
//                << res_->norm()           << "  " 
//                << lambda_->norm()  << "  " 
//                << flagCR_          << "  " 
//                << iterCR_          << "\n";
      if ( xtmp_->norm() < gtol_*algo_state.gnorm ) {
        flag_ = 0;
        break;
      }
      if ( s.norm() < stol_*x.norm() ) {
        flag_ = 2;
        break;
      } 
    }
    if ( iter_ == maxit_ ) {
      flag_ = 1;
    }
    else {
      iter_++;
    }
  }