ROL
ROL_DoubleDogLeg_U.hpp
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43
44#ifndef ROL_DOUBLEDOGLEG_U_H
45#define ROL_DOUBLEDOGLEG_U_H
46
51#include "ROL_TrustRegion_U.hpp"
52#include "ROL_Types.hpp"
53
54namespace ROL {
55
56template<class Real>
57class DoubleDogLeg_U : public TrustRegion_U<Real> {
58private:
59
60 Ptr<Vector<Real>> primal_, dual_;
61
62public:
63
65
66 void initialize(const Vector<Real> &x, const Vector<Real> &g) {
67 primal_ = x.clone();
68 dual_ = g.clone();
69 }
70
72 Real &snorm,
73 Real &pRed,
74 int &iflag,
75 int &iter,
76 const Real del,
78 Real tol = std::sqrt(ROL_EPSILON<Real>());
79 const Real one(1), zero(0), half(0.5), p2(0.2), p8(0.8), two(2);
80 // Set s to be the (projected) gradient
81 s.set(model.getGradient()->dual());
82 // Compute (quasi-)Newton step
83 model.invHessVec(*primal_,*model.getGradient(),s,tol);
84 Real sNnorm = primal_->norm();
85 Real tmp = -primal_->dot(s);
86 Real gsN = std::abs(tmp);
87 // Check if (quasi-)Newton step is feasible
88 if ( tmp >= zero ) {
89 // Use the Cauchy point
90 model.hessVec(*dual_,s,s,tol);
91 //Real gBg = dual_->dot(s.dual());
92 Real gBg = dual_->apply(s);
93 Real gnorm = s.dual().norm();
94 Real gg = gnorm*gnorm;
95 Real alpha = del/gnorm;
96 if ( gBg > ROL_EPSILON<Real>() ) {
97 alpha = std::min(gg/gBg, del/gnorm);
98 }
99 s.scale(-alpha);
100 snorm = alpha*gnorm;
101 iflag = 2;
102 pRed = alpha*(gg - half*alpha*gBg);
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(*primal_);
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(*dual_,s,s,tol);
115 Real alpha = zero;
116 Real beta = zero;
117 Real gnorm = s.norm();
118 Real gnorm2 = gnorm*gnorm;
119 //Real gBg = dual_->dot(s.dual());
120 Real gBg = dual_->apply(s);
121 Real gamma1 = gnorm/gBg;
122 Real gamma2 = gnorm/gsN;
123 Real eta = p8*gamma1*gamma2 + p2;
124 if (eta*sNnorm <= del || gBg <= zero) { // Dogleg Point is inside trust region
125 alpha = del/sNnorm;
126 beta = zero;
127 s.set(*primal_);
128 s.scale(-alpha);
129 snorm = del;
130 iflag = 1;
131 }
132 else {
133 if (gnorm2*gamma1 >= del) { // Cauchy Point is outside trust region
134 alpha = zero;
135 beta = -del/gnorm;
136 s.scale(beta);
137 snorm = del;
138 iflag = 2;
139 }
140 else { // Find convex combination of Cauchy and Dogleg point
141 s.scale(-gamma1*gnorm);
142 primal_->scale(eta);
143 primal_->plus(s);
144 primal_->scale(-one);
145 Real wNorm = primal_->dot(*primal_);
146 Real sigma = del*del-std::pow(gamma1*gnorm,two);
147 Real phi = s.dot(*primal_);
148 Real theta = (-phi + std::sqrt(phi*phi+wNorm*sigma))/wNorm;
149 s.axpy(theta,*primal_);
150 snorm = del;
151 alpha = theta*eta;
152 beta = (one-theta)*(-gamma1*gnorm);
153 iflag = 3;
154 }
155 }
156 pRed = -(alpha*(half*alpha-one)*gsN + half*beta*beta*gBg + beta*(one-alpha)*gnorm2);
157 }
158 }
159 }
160};
161
162} // namespace ROL
163
164#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 solve(Vector< Real > &s, Real &snorm, Real &pRed, int &iflag, int &iter, const Real del, TrustRegionModel_U< Real > &model)
void initialize(const Vector< Real > &x, const Vector< Real > &g)
Ptr< Vector< Real > > dual_
Ptr< Vector< Real > > primal_
Provides the interface to evaluate trust-region model functions.
virtual void hessVec(Vector< Real > &hv, const Vector< Real > &v, const Vector< Real > &s, Real &tol) override
Apply Hessian approximation to vector.
virtual void invHessVec(Vector< Real > &hv, const Vector< Real > &v, const Vector< Real > &s, Real &tol) override
Apply inverse Hessian approximation to vector.
virtual const Ptr< const Vector< Real > > getGradient(void) const
Provides interface for and implements trust-region subproblem solvers.
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 .