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
54namespace ROL {
55
56template<class Real>
57class DoubleDogLeg : public TrustRegion<Real> {
58private:
59
60 ROL::Ptr<CauchyPoint<Real> > cpt_;
61
62 ROL::Ptr<Vector<Real> > s_;
63 ROL::Ptr<Vector<Real> > v_;
64 ROL::Ptr<Vector<Real> > Hp_;
65
66 Real pRed_;
67
68public:
69
70 // Constructor
71 DoubleDogLeg( ROL::ParameterList &parlist ) : TrustRegion<Real>(parlist), pRed_(0) {
72 cpt_ = ROL::makePtr<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 v_ = s.clone();
80 Hp_ = g.clone();
81 }
82
83 void run( Vector<Real> &s,
84 Real &snorm,
85 int &iflag,
86 int &iter,
87 const Real del,
88 TrustRegionModel<Real> &model ) {
89 Real tol = std::sqrt(ROL_EPSILON<Real>());
90 const Real one(1), zero(0), half(0.5), p2(0.2), p8(0.8), two(2);
91 // Set s to be the (projected) gradient
92 model.dualTransform(*Hp_,*model.getGradient());
93 s.set(Hp_->dual());
94 // Compute (quasi-)Newton step
95 model.invHessVec(*s_,*Hp_,s,tol);
96 Real sNnorm = s_->norm();
97 Real tmp = -s_->dot(s);
98 bool negCurv = (tmp > zero ? true : false);
99 Real gsN = std::abs(tmp);
100 // Check if (quasi-)Newton step is feasible
101 if ( negCurv ) {
102 // Use Cauchy point
103 cpt_->run(s,snorm,iflag,iter,del,model);
104 pRed_ = cpt_->getPredictedReduction();
105 iflag = 2;
106 }
107 else {
108 // Approximately solve trust region subproblem using double dogleg curve
109 if (sNnorm <= del) { // Use the (quasi-)Newton step
110 s.set(*s_);
111 s.scale(-one);
112 snorm = sNnorm;
113 pRed_ = half*gsN;
114 iflag = 0;
115 }
116 else { // The (quasi-)Newton step is outside of trust region
117 model.hessVec(*Hp_,s,s,tol);
118 Real alpha = zero;
119 Real beta = zero;
120 Real gnorm = s.norm();
121 Real gnorm2 = gnorm*gnorm;
122 Real gBg = Hp_->dot(s.dual());
123 Real gamma1 = gnorm/gBg;
124 Real gamma2 = gnorm/gsN;
125 Real eta = p8*gamma1*gamma2 + p2;
126 if (eta*sNnorm <= del || gBg <= zero) { // Dogleg Point is inside trust region
127 alpha = del/sNnorm;
128 beta = zero;
129 s.set(*s_);
130 s.scale(-alpha);
131 snorm = del;
132 iflag = 1;
133 }
134 else {
135 if (gnorm2*gamma1 >= del) { // Cauchy Point is outside trust region
136 alpha = zero;
137 beta = -del/gnorm;
138 s.scale(beta);
139 snorm = del;
140 iflag = 2;
141 }
142 else { // Find convex combination of Cauchy and Dogleg point
143 s.scale(-gamma1*gnorm);
144 v_->set(s);
145 v_->axpy(eta,*s_);
146 v_->scale(-one);
147 Real wNorm = v_->dot(*v_);
148 Real sigma = del*del-std::pow(gamma1*gnorm,two);
149 Real phi = s.dot(*v_);
150 Real theta = (-phi + std::sqrt(phi*phi+wNorm*sigma))/wNorm;
151 s.axpy(theta,*v_);
152 snorm = del;
153 alpha = theta*eta;
154 beta = (one-theta)*(-gamma1*gnorm);
155 iflag = 3;
156 }
157 }
158 pRed_ = -(alpha*(half*alpha-one)*gsN + half*beta*beta*gBg + beta*(one-alpha)*gnorm2);
159 }
160 }
161 model.primalTransform(*s_,s);
162 s.set(*s_);
163 snorm = s.norm();
165 }
166};
167
168}
169
170#endif
Objective_SerialSimOpt(const Ptr< Obj > &obj, const V &ui) z0_ zero()
Contains definitions of custom data types in ROL.
Provides interface for the double dog leg trust-region subproblem solver.
void run(Vector< Real > &s, Real &snorm, int &iflag, int &iter, const Real del, TrustRegionModel< Real > &model)
ROL::Ptr< Vector< Real > > s_
DoubleDogLeg(ROL::ParameterList &parlist)
void initialize(const Vector< Real > &x, const Vector< Real > &s, const Vector< Real > &g)
ROL::Ptr< Vector< Real > > Hp_
ROL::Ptr< Vector< Real > > v_
ROL::Ptr< CauchyPoint< Real > > cpt_
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.
Definition: ROL_Vector.hpp:84
virtual Real norm() const =0
Returns where .
virtual void set(const Vector &x)
Set where .
Definition: ROL_Vector.hpp:209
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,...
Definition: ROL_Vector.hpp:226
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 .
Definition: ROL_Vector.hpp:153
virtual Real dot(const Vector &x) const =0
Compute where .