ROL
ROL_DoubleDogLeg.hpp
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43 
44 #ifndef ROL_DOUBLEDOGLEG_H
45 #define ROL_DOUBLEDOGLEG_H
46 
51 #include "ROL_TrustRegion.hpp"
52 #include "ROL_Types.hpp"
53 #include "ROL_HelperFunctions.hpp"
54 
55 namespace ROL {
56 
57 template<class Real>
58 class DoubleDogLeg : public TrustRegion<Real> {
59 private:
60 
61  Teuchos::RCP<CauchyPoint<Real> > cpt_;
62 
63  Teuchos::RCP<Vector<Real> > s_;
64  Teuchos::RCP<Vector<Real> > v_;
65  Teuchos::RCP<Vector<Real> > Hp_;
66 
67  Real pRed_;
68 
69 public:
70 
71  // Constructor
72  DoubleDogLeg( Teuchos::ParameterList &parlist ) : TrustRegion<Real>(parlist), pRed_(0.0) {
73  cpt_ = Teuchos::rcp(new CauchyPoint<Real>(parlist));
74  }
75 
76  void initialize( const Vector<Real> &x, const Vector<Real> &s, const Vector<Real> &g) {
78  cpt_->initialize(x,s,g);
79  s_ = s.clone();
80  v_ = s.clone();
81  Hp_ = g.clone();
82  }
83 
84  void run( Vector<Real> &s, Real &snorm, Real &del, int &iflag, int &iter, const Vector<Real> &x,
85  const Vector<Real> &grad, const Real &gnorm, ProjectedObjective<Real> &pObj ) {
86  Real tol = std::sqrt(ROL_EPSILON);
87 
88  // Compute quasi-Newton step
89  pObj.reducedInvHessVec(*s_,grad,x,grad,x,tol);
90  s_->scale(-1.0);
91  Real sNnorm = s_->norm();
92  Real tmp = s_->dot(grad.dual());
93  bool negCurv = false;
94  if ( tmp >= 0.0 ) {
95  negCurv = true;
96  }
97  Real gsN = std::abs(tmp);
98 
99  if ( negCurv ) {
100  cpt_->run(s,snorm,del,iflag,iter,x,grad,gnorm,pObj);
101  pRed_ = cpt_->getPredictedReduction();
102  iflag = 2;
103  }
104  else {
105  // Approximately solve trust region subproblem using double dogleg curve
106  if (sNnorm <= del) { // Use the quasi-Newton step
107  s.set(*s_);
108  snorm = sNnorm;
109  pRed_ = 0.5*gsN;
110  iflag = 0;
111  }
112  else { // quasi-Newton step is outside of trust region
113  pObj.reducedHessVec(*Hp_,grad.dual(),x,grad,x,tol);
114  Real alpha = 0.0;
115  Real beta = 0.0;
116  Real gnorm2 = gnorm*gnorm;
117  Real gBg = grad.dot(*Hp_);
118  Real gamma1 = gnorm/gBg;
119  Real gamma2 = gnorm/gsN;
120  Real eta = 0.8*gamma1*gamma2 + 0.2;
121  if (eta*sNnorm <= del || gBg <= 0.0) { // Dogleg Point is inside trust region
122  alpha = del/sNnorm;
123  beta = 0.0;
124  s.set(*s_);
125  s.scale(alpha);
126  snorm = del;
127  iflag = 1;
128  }
129  else {
130  if (gnorm2*gamma1 >= del) { // Cauchy Point is outside trust region
131  alpha = 0.0;
132  beta = -del/gnorm;
133  s.set(grad.dual());
134  s.scale(beta);
135  snorm = del;
136  iflag = 2;
137  }
138  else { // Find convex combination of Cauchy and Dogleg point
139  s.set(grad.dual());
140  s.scale(-gamma1*gnorm);
141  v_->set(s);
142  v_->scale(-1.0);
143  v_->axpy(eta,*s_);
144  Real wNorm = v_->dot(*v_);
145  Real sigma = del*del-std::pow(gamma1*gnorm,2.0);
146  Real phi = s.dot(*v_);
147  Real theta = (-phi + std::sqrt(phi*phi+wNorm*sigma))/wNorm;
148  s.axpy(theta,*v_);
149  snorm = del;
150  alpha = theta*eta;
151  beta = (1.0-theta)*(-gamma1*gnorm);
152  iflag = 3;
153  }
154  }
155  pRed_ = -(alpha*(0.5*alpha-1)*gsN + 0.5*beta*beta*gBg + beta*(1-alpha)*gnorm2);
156  }
158  }
159  }
160 };
161 
162 }
163 
164 #endif
Teuchos::RCP< CauchyPoint< Real > > cpt_
void initialize(const Vector< Real > &x, const Vector< Real > &s, const Vector< Real > &g)
virtual const Vector & dual() const
Return dual representation of , for example, the result of applying a Riesz map, or change of basis...
Definition: ROL_Vector.hpp:213
virtual void scale(const Real alpha)=0
Compute where .
virtual void axpy(const Real alpha, const Vector &x)
Compute where .
Definition: ROL_Vector.hpp:143
void run(Vector< Real > &s, Real &snorm, Real &del, int &iflag, int &iter, const Vector< Real > &x, const Vector< Real > &grad, const Real &gnorm, ProjectedObjective< Real > &pObj)
virtual void initialize(const Vector< Real > &x, const Vector< Real > &s, const Vector< Real > &g)
void reducedHessVec(Vector< Real > &Hv, const Vector< Real > &v, const Vector< Real > &p, const Vector< Real > &d, const Vector< Real > &x, Real &tol)
Apply the reduced Hessian to a vector, v. The reduced Hessian first removes elements of v correspondi...
Contains definitions of custom data types in ROL.
virtual Teuchos::RCP< Vector > clone() const =0
Clone to make a new (uninitialized) vector.
Provides interface for and implements trust-region subproblem solvers.
Contains definitions for helper functions in ROL.
Defines the linear algebra or vector space interface.
Definition: ROL_Vector.hpp:74
virtual Real dot(const Vector &x) const =0
Compute where .
Provides interface for the double dog leg trust-region subproblem solver.
Teuchos::RCP< Vector< Real > > s_
DoubleDogLeg(Teuchos::ParameterList &parlist)
void setPredictedReduction(const Real pRed)
void reducedInvHessVec(Vector< Real > &Hv, const Vector< Real > &v, const Vector< Real > &p, const Vector< Real > &d, const Vector< Real > &x, Real &tol)
Apply the reduced inverse Hessian to a vector, v. The reduced inverse Hessian first removes elements ...
Teuchos::RCP< Vector< Real > > v_
Provides interface for the Cauchy point trust-region subproblem solver.
virtual void set(const Vector &x)
Set where .
Definition: ROL_Vector.hpp:196
static const double ROL_EPSILON
Platform-dependent machine epsilon.
Definition: ROL_Types.hpp:118
Teuchos::RCP< Vector< Real > > Hp_