ROL
ROL_CubicInterp.hpp
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43
44#ifndef ROL_CUBICINTERP_H
45#define ROL_CUBICINTERP_H
46
51#include "ROL_LineSearch.hpp"
52
53namespace ROL {
54
55template<class Real>
56class CubicInterp : public LineSearch<Real> {
57private:
58 Real rho_;
59 ROL::Ptr<Vector<Real> > xnew_;
60
61public:
62
63 virtual ~CubicInterp() {}
64
65 // Constructor
66 CubicInterp( ROL::ParameterList &parlist ) : LineSearch<Real>(parlist) {
67 Real half(0.5);
68 rho_ = parlist.sublist("Step").sublist("Line Search").sublist("Line-Search Method").get("Backtracking Rate",half);
69 }
70
71 void initialize( const Vector<Real> &x, const Vector<Real> &s, const Vector<Real> &g,
73 LineSearch<Real>::initialize(x,s,g,obj,con);
74 xnew_ = x.clone();
75 }
76
77 void run( Real &alpha, Real &fval, int &ls_neval, int &ls_ngrad,
78 const Real &gs, const Vector<Real> &s, const Vector<Real> &x,
80 Real tol = std::sqrt(ROL_EPSILON<Real>());
81 ls_neval = 0;
82 ls_ngrad = 0;
83 // Get initial line search parameter
84 alpha = LineSearch<Real>::getInitialAlpha(ls_neval,ls_ngrad,fval,gs,x,s,obj,con);
85 // Update iterate
87 // Get objective value at xnew
88 Real fold = fval;
89 obj.update(*xnew_);
90 fval = obj.value(*xnew_,tol);
91 ls_neval++;
92 // Initialize
93 Real fvalp(0), alpha1(0), alpha2(0), a(0), b(0), x1(0), x2(0);
94 const Real one(1), two(2), three(3), half(0.5), p1(0.1);
95 bool first_iter = true;
96 // Perform cubic interpolation back tracking
97 while ( !LineSearch<Real>::status(LINESEARCH_CUBICINTERP,ls_neval,ls_ngrad,alpha,fold,gs,fval,x,s,obj,con) ) {
98 if ( first_iter ) { // Minimize quadratic interpolate
99 alpha1 = -gs*alpha*alpha/(two*(fval-fold-gs*alpha));
100 first_iter = false;
101 }
102 else { // Minimize cubic interpolate
103 x1 = fval-fold-alpha*gs;
104 x2 = fvalp-fval-alpha2*gs;
105 a = (one/(alpha - alpha2))*( x1/(alpha*alpha) - x2/(alpha2*alpha2));
106 b = (one/(alpha - alpha2))*(-x1*alpha2/(alpha*alpha) + x2*alpha/(alpha2*alpha2));
107 if ( std::abs(a) < ROL_EPSILON<Real>() ) {
108 alpha1 = -gs/(two*b);
109 }
110 else {
111 alpha1 = (-b+sqrt(b*b-three*a*gs))/(three*a);
112 }
113 if ( alpha1 > half*alpha ) {
114 alpha1 = half*alpha;
115 }
116 }
117 alpha2 = alpha;
118 fvalp = fval;
119 // Back track if necessary
120 if ( alpha1 <= p1*alpha ) {
121 alpha *= p1;
122 }
123 else if ( alpha1 >= half*alpha ) {
124 alpha *= half;
125 }
126 else {
127 alpha = alpha1;
128 }
129 // Update iterate
131 // Get objective value at xnew
132 obj.update(*xnew_);
133 fval = obj.value(*xnew_,tol);
134 ls_neval++;
135 }
136 }
137};
138
139}
140
141#endif
Provides the interface to apply upper and lower bound constraints.
Implements cubic interpolation back tracking line search.
void initialize(const Vector< Real > &x, const Vector< Real > &s, const Vector< Real > &g, Objective< Real > &obj, BoundConstraint< Real > &con)
ROL::Ptr< Vector< Real > > xnew_
CubicInterp(ROL::ParameterList &parlist)
void run(Real &alpha, Real &fval, int &ls_neval, int &ls_ngrad, const Real &gs, const Vector< Real > &s, const Vector< Real > &x, Objective< Real > &obj, BoundConstraint< Real > &con)
Provides interface for and implements line searches.
void updateIterate(Vector< Real > &xnew, const Vector< Real > &x, const Vector< Real > &s, Real alpha, BoundConstraint< Real > &con)
virtual void initialize(const Vector< Real > &x, const Vector< Real > &s, const Vector< Real > &g, Objective< Real > &obj, BoundConstraint< Real > &con)
virtual Real getInitialAlpha(int &ls_neval, int &ls_ngrad, const Real fval, const Real gs, const Vector< Real > &x, const Vector< Real > &s, Objective< Real > &obj, BoundConstraint< Real > &con)
Provides the interface to evaluate objective functions.
virtual Real value(const Vector< Real > &x, Real &tol)=0
Compute value.
virtual void update(const Vector< Real > &x, UpdateType type, int iter=-1)
Update objective function.
Defines the linear algebra or vector space interface.
virtual ROL::Ptr< Vector > clone() const =0
Clone to make a new (uninitialized) vector.
@ LINESEARCH_CUBICINTERP