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
54namespace ROL {
55
56template<class Real>
57class DogLeg : public TrustRegion<Real> {
58private:
59
60 ROL::Ptr<CauchyPoint<Real> > cpt_;
61
62 ROL::Ptr<Vector<Real> > s_;
63 ROL::Ptr<Vector<Real> > Hp_;
64
65 Real pRed_;
66
67public:
68
69 // Constructor
70 DogLeg( ROL::ParameterList &parlist ) : TrustRegion<Real>(parlist), pRed_(0) {
71 cpt_ = ROL::makePtr<CauchyPoint<Real>>(parlist);
72 }
73
74 void initialize( const Vector<Real> &x, const Vector<Real> &s, const Vector<Real> &g) {
76 cpt_->initialize(x,s,g);
77 s_ = s.clone();
78 Hp_ = g.clone();
79 }
80
81 void run( Vector<Real> &s,
82 Real &snorm,
83 int &iflag,
84 int &iter,
85 const Real del,
86 TrustRegionModel<Real> &model ) {
87 Real tol = std::sqrt(ROL_EPSILON<Real>());
88 const Real zero(0), half(0.5), one(1), two(2);
89 // Set s to be the (projected) gradient
90 model.dualTransform(*Hp_,*model.getGradient());
91 s.set(Hp_->dual());
92 // Compute (quasi-)Newton step
93 model.invHessVec(*s_,*Hp_,s,tol);
94 Real sNnorm = s_->norm();
95 Real gsN = -s_->dot(s);
96 bool negCurv = (gsN > zero ? true : false);
97 // Check if (quasi-)Newton step is feasible
98 if ( negCurv ) {
99 // Use Cauchy point
100 cpt_->run(s,snorm,iflag,iter,del,model);
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 s.scale(-one);
109 snorm = sNnorm;
110 pRed_ = -half*gsN;
111 iflag = 0;
112 }
113 else { // The (quasi-)Newton step is outside of trust region
114 model.hessVec(*Hp_,s,s,tol);
115 Real alpha = zero;
116 Real beta = zero;
117 Real gnorm = s.norm();
118 Real gnorm2 = gnorm*gnorm;
119 Real gBg = Hp_->dot(s.dual());
120 Real gamma = gnorm2/gBg;
121 if ( gamma*gnorm >= del || gBg <= zero ) {
122 // Use Cauchy point
123 alpha = zero;
124 beta = del/gnorm;
125 s.scale(-beta);
126 snorm = del;
127 iflag = 2;
128 }
129 else {
130 // Use a convex combination of Cauchy point and (quasi-)Newton step
131 Real a = sNnorm*sNnorm + two*gamma*gsN + gamma*gamma*gnorm2;
132 Real b = -gamma*gsN - gamma*gamma*gnorm2;
133 Real c = gamma*gamma*gnorm2 - del*del;
134 alpha = (-b + sqrt(b*b - a*c))/a;
135 beta = gamma*(one-alpha);
136 s.scale(-beta);
137 s.axpy(-alpha,*s_);
138 snorm = del;
139 iflag = 1;
140 }
141 pRed_ = (alpha*(half*alpha-one)*gsN - half*beta*beta*gBg + beta*(one-alpha)*gnorm2);
142 }
143 }
144 model.primalTransform(*s_,s);
145 s.set(*s_);
146 snorm = s.norm();
147 // Update predicted reduction
149 }
150};
151
152}
153
154#endif
Objective_SerialSimOpt(const Ptr< Obj > &obj, const V &ui) z0 zero)()
Contains definitions of custom data types in ROL.
Provides interface for dog leg trust-region subproblem solver.
DogLeg(ROL::ParameterList &parlist)
void initialize(const Vector< Real > &x, const Vector< Real > &s, const Vector< Real > &g)
ROL::Ptr< Vector< Real > > Hp_
ROL::Ptr< CauchyPoint< Real > > cpt_
ROL::Ptr< Vector< Real > > s_
void run(Vector< Real > &s, Real &snorm, int &iflag, int &iter, const Real del, TrustRegionModel< Real > &model)
Provides the interface to evaluate trust-region model functions.
virtual void dualTransform(Vector< Real > &tv, const Vector< Real > &v)
virtual const Ptr< const Vector< Real > > getGradient(void) const
virtual void primalTransform(Vector< Real > &tv, const Vector< Real > &v)
virtual void hessVec(Vector< Real > &hv, const Vector< Real > &v, const Vector< Real > &s, Real &tol)
Apply Hessian approximation to vector.
virtual void invHessVec(Vector< Real > &hv, const Vector< Real > &v, const Vector< Real > &s, Real &tol)
Apply inverse Hessian approximation to vector.
Provides interface for and implements trust-region subproblem solvers.
virtual void initialize(const Vector< Real > &x, const Vector< Real > &s, const Vector< Real > &g)
void setPredictedReduction(const Real pRed)
Defines the linear algebra or vector space interface.
virtual Real norm() const =0
Returns where .
virtual void set(const Vector &x)
Set where .
virtual void scale(const Real alpha)=0
Compute where .
virtual const Vector & dual() const
Return dual representation of , for example, the result of applying a Riesz map, or change of basis,...
virtual ROL::Ptr< Vector > clone() const =0
Clone to make a new (uninitialized) vector.
virtual void axpy(const Real alpha, const Vector &x)
Compute where .