ROL
ROL_DogLeg.hpp
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43 
44 #ifndef ROL_DOGLEG_H
45 #define ROL_DOGLEG_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 DogLeg : public TrustRegion<Real> {
59 private:
60 
61  Teuchos::RCP<CauchyPoint<Real> > cpt_;
62 
63  Teuchos::RCP<Vector<Real> > s_;
64  Teuchos::RCP<Vector<Real> > Hp_;
65 
66  Real pRed_;
67 
68 public:
69 
70  // Constructor
71  DogLeg( Teuchos::ParameterList &parlist ) : TrustRegion<Real>(parlist), pRed_(0.0) {
72  cpt_ = Teuchos::rcp(new CauchyPoint<Real>(parlist));
73  }
74 
75  void initialize( const Vector<Real> &x, const Vector<Real> &s, const Vector<Real> &g) {
77  cpt_->initialize(x,s,g);
78  s_ = s.clone();
79  Hp_ = g.clone();
80  }
81 
82  void run( Vector<Real> &s, Real &snorm, Real &del, int &iflag, int &iter, const Vector<Real> &x,
83  const Vector<Real> &grad, const Real &gnorm, ProjectedObjective<Real> &pObj ) {
84  Real tol = std::sqrt(ROL_EPSILON);
85  // Compute quasi-Newton step
86  pObj.reducedInvHessVec(*s_,grad,x,grad,x,tol);
87  s_->scale(-1.0);
88  Real sNnorm = s_->norm();
89  Real gsN = s_->dot(grad.dual());
90  bool negCurv = false;
91  if ( gsN >= 0.0 ) {
92  negCurv = true;
93  }
94 
95  if ( negCurv ) {
96  cpt_->run(s,snorm,del,iflag,iter,x,grad,gnorm,pObj);
97  pRed_ = cpt_->getPredictedReduction();
98  iflag = 2;
99  }
100  else {
101  // Approximately solve trust region subproblem using double dogleg curve
102  if (sNnorm <= del) { // Use the quasi-Newton step
103  s.set(*s_);
104  snorm = sNnorm;
105  pRed_ = -0.5*gsN;
106  iflag = 0;
107  }
108  else { // quasi-Newton step is outside of trust region
109  pObj.reducedHessVec(*Hp_,grad.dual(),x,grad,x,tol);
110  Real alpha = 0.0;
111  Real beta = 0.0;
112  Real gnorm2 = gnorm*gnorm;
113  Real gBg = grad.dot(*Hp_);
114  Real gamma = gnorm2/gBg;
115  if ( gamma*gnorm >= del || gBg <= 0.0 ) {
116  alpha = 0.0;
117  beta = del/gnorm;
118  s.set(grad.dual());
119  s.scale(-beta);
120  snorm = del;
121  iflag = 2;
122  }
123  else {
124  Real a = sNnorm*sNnorm + 2.0*gamma*gsN + gamma*gamma*gnorm2;
125  Real b = -gamma*gsN - gamma*gamma*gnorm2;
126  Real c = gamma*gamma*gnorm2 - del*del;
127  alpha = (-b + sqrt(b*b - a*c))/a;
128  beta = gamma*(1.0-alpha);
129  s.set(grad.dual());
130  s.scale(-beta);
131  s.axpy(alpha,*s_);
132  snorm = del;
133  iflag = 1;
134  }
135  pRed_ = (alpha*(0.5*alpha-1)*gsN - 0.5*beta*beta*gBg + beta*(1-alpha)*gnorm2);
136  }
137  }
139  }
140 };
141 
142 }
143 
144 #endif
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
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
Teuchos::RCP< Vector< Real > > Hp_
Definition: ROL_DogLeg.hpp:64
Teuchos::RCP< CauchyPoint< Real > > cpt_
Definition: ROL_DogLeg.hpp:61
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)
Definition: ROL_DogLeg.hpp:82
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 > > s_
Definition: ROL_DogLeg.hpp:63
Provides interface for dog leg trust-region subproblem solver.
Definition: ROL_DogLeg.hpp:58
Provides interface for the Cauchy point trust-region subproblem solver.
virtual void set(const Vector &x)
Set where .
Definition: ROL_Vector.hpp:196
void initialize(const Vector< Real > &x, const Vector< Real > &s, const Vector< Real > &g)
Definition: ROL_DogLeg.hpp:75
DogLeg(Teuchos::ParameterList &parlist)
Definition: ROL_DogLeg.hpp:71
static const double ROL_EPSILON
Platform-dependent machine epsilon.
Definition: ROL_Types.hpp:118