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 
53 namespace ROL {
54 
55 template<class Real>
56 class CubicInterp : public LineSearch<Real> {
57 private:
58  Real rho_;
59  Teuchos::RCP<Vector<Real> > xnew_;
60 
61 public:
62 
63  virtual ~CubicInterp() {}
64 
65  // Constructor
66  CubicInterp( Teuchos::ParameterList &parlist ) : LineSearch<Real>(parlist) {
67  rho_ = parlist.sublist("Step").sublist("Line Search").sublist("Line-Search Method").get("Backtracking Rate",0.5);
68  }
69 
70  void initialize( const Vector<Real> &x, const Vector<Real> &s, const Vector<Real> &g,
72  LineSearch<Real>::initialize(x,s,g,obj,con);
73  xnew_ = x.clone();
74  }
75 
76  void run( Real &alpha, Real &fval, int &ls_neval, int &ls_ngrad,
77  const Real &gs, const Vector<Real> &s, const Vector<Real> &x,
79  Real tol = std::sqrt(ROL_EPSILON);
80  ls_neval = 0;
81  ls_ngrad = 0;
82  // Get initial line search parameter
83  alpha = LineSearch<Real>::getInitialAlpha(ls_neval,ls_ngrad,fval,gs,x,s,obj,con);
84  // Update iterate
85  LineSearch<Real>::updateIterate(*xnew_,x,s,alpha,con);
86  // Get objective value at xnew
87  Real fold = fval;
88  obj.update(*xnew_);
89  fval = obj.value(*xnew_,tol);
90  ls_neval++;
91  // Initialize
92  Real fvalp = 0.0;
93  Real alpha1 = 0.0;
94  Real alpha2 = 0.0;
95  Real a = 0.0;
96  Real b = 0.0;
97  Real x1 = 0.0;
98  Real x2 = 0.0;
99  bool first_iter = true;
100  // Perform cubic interpolation back tracking
101  while ( !LineSearch<Real>::status(LINESEARCH_CUBICINTERP,ls_neval,ls_ngrad,alpha,fold,gs,fval,x,s,obj,con) ) {
102  if ( first_iter ) { // Minimize quadratic interpolate
103  alpha1 = -gs*alpha*alpha/(2.0*(fval-fold-gs*alpha));
104  first_iter = false;
105  }
106  else { // Minimize cubic interpolate
107  x1 = fval-fold-alpha*gs;
108  x2 = fvalp-fval-alpha2*gs;
109  a = (1.0/(alpha - alpha2))*( x1/(alpha*alpha) - x2/(alpha2*alpha2));
110  b = (1.0/(alpha - alpha2))*(-x1*alpha2/(alpha*alpha) + x2*alpha/(alpha2*alpha2));
111  if ( std::abs(a) < ROL_EPSILON ) {
112  alpha1 = -gs/(2.0*b);
113  }
114  else {
115  alpha1 = (-b+sqrt(b*b-3.0*a*gs))/(3.0*a);
116  }
117  if ( alpha1 > 0.5*alpha ) {
118  alpha1 = 0.5*alpha;
119  }
120  }
121  alpha2 = alpha;
122  fvalp = fval;
123  // Back track if necessary
124  if ( alpha1 <= 0.1*alpha ) {
125  alpha *= 0.1;
126  }
127  else if ( alpha1 >= 0.5*alpha ) {
128  alpha *= 0.5;
129  }
130  else {
131  alpha = alpha1;
132  }
133  // Update iterate
134  LineSearch<Real>::updateIterate(*xnew_,x,s,alpha,con);
135  // Get objective value at xnew
136  obj.update(*xnew_);
137  fval = obj.value(*xnew_,tol);
138  ls_neval++;
139  }
140  }
141 };
142 
143 }
144 
145 #endif
Provides the interface to evaluate objective functions.
void updateIterate(Vector< Real > &xnew, const Vector< Real > &x, const Vector< Real > &s, Real alpha, 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)
CubicInterp(Teuchos::ParameterList &parlist)
virtual Real value(const Vector< Real > &x, Real &tol)=0
Compute value.
void initialize(const Vector< Real > &x, const Vector< Real > &s, const Vector< Real > &g, Objective< Real > &obj, BoundConstraint< Real > &con)
virtual Teuchos::RCP< Vector > clone() const =0
Clone to make a new (uninitialized) vector.
Teuchos::RCP< Vector< Real > > xnew_
Defines the linear algebra or vector space interface.
Definition: ROL_Vector.hpp:74
Provides interface for and implements line searches.
Implements cubic interpolation back tracking line search.
Provides the interface to apply upper and lower bound constraints.
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)
virtual void update(const Vector< Real > &x, bool flag=true, int iter=-1)
Update objective function.
virtual void initialize(const Vector< Real > &x, const Vector< Real > &s, const Vector< Real > &g, Objective< Real > &obj, BoundConstraint< Real > &con)
static const double ROL_EPSILON
Platform-dependent machine epsilon.
Definition: ROL_Types.hpp:118