ROL
ROL_CubicInterp_U.hpp
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1 // @HEADER
2 // *****************************************************************************
3 // Rapid Optimization Library (ROL) Package
4 //
5 // Copyright 2014 NTESS and the ROL contributors.
6 // SPDX-License-Identifier: BSD-3-Clause
7 // *****************************************************************************
8 // @HEADER
9 
10 #ifndef ROL_CUBICINTERP_U_H
11 #define ROL_CUBICINTERP_U_H
12 
17 #include "ROL_LineSearch_U.hpp"
18 
19 namespace ROL {
20 
21 template<typename Real>
22 class CubicInterp_U : public LineSearch_U<Real> {
23 private:
24  Real rho_;
25  Ptr<Vector<Real>> xnew_;
26 
29 
30 public:
31 
32  CubicInterp_U( ParameterList &parlist ) : LineSearch_U<Real>(parlist) {
33  const Real half(0.5);
34  rho_ = parlist.sublist("Step").sublist("Line Search").sublist("Line-Search Method").get("Backtracking Rate",half);
35  }
36 
37  void initialize(const Vector<Real> &x, const Vector<Real> &g) override {
39  xnew_ = x.clone();
40  }
41 
42  void run( Real &alpha, Real &fval, int &ls_neval, int &ls_ngrad,
43  const Real &gs, const Vector<Real> &s, const Vector<Real> &x,
44  Objective<Real> &obj ) override {
45  Real tol = std::sqrt(ROL_EPSILON<Real>());
46  ls_neval = 0;
47  ls_ngrad = 0;
48  // Get initial line search parameter
49  alpha = getInitialAlpha(ls_neval,ls_ngrad,fval,gs,x,s,obj);
50  // Update iterate
51  xnew_->set(x); xnew_->axpy(alpha,s);
52  // Get objective value at xnew
53  Real fold = fval;
55  fval = obj.value(*xnew_,tol);
56  ls_neval++;
57  // Initialize
58  Real fvalp(0), alpha1(0), alpha2(0), a(0), b(0), x1(0), x2(0);
59  const Real one(1), two(2), three(3), half(0.5), p1(0.1);
60  bool first_iter = true;
61  // Perform cubic interpolation back tracking
62  while (!status(LINESEARCH_U_CUBICINTERP,ls_neval,ls_ngrad,alpha,fold,gs,fval,x,s,obj)) {
63  if (first_iter) { // Minimize quadratic interpolate
64  alpha1 = -gs*alpha*alpha/(two*(fval-fold-gs*alpha));
65  first_iter = false;
66  }
67  else { // Minimize cubic interpolate
68  x1 = fval-fold-alpha*gs;
69  x2 = fvalp-fval-alpha2*gs;
70  a = (one/(alpha - alpha2))*( x1/(alpha*alpha) - x2/(alpha2*alpha2));
71  b = (one/(alpha - alpha2))*(-x1*alpha2/(alpha*alpha) + x2*alpha/(alpha2*alpha2));
72  if (std::abs(a) < ROL_EPSILON<Real>()) {
73  alpha1 = -gs/(two*b);
74  }
75  else {
76  alpha1 = (-b+sqrt(b*b-three*a*gs))/(three*a);
77  }
78  if ( alpha1 > half*alpha ) {
79  alpha1 = half*alpha;
80  }
81  }
82  alpha2 = alpha;
83  fvalp = fval;
84  // Back track if necessary
85  if (alpha1 <= p1*alpha) {
86  alpha *= p1;
87  }
88  else if (alpha1 >= half*alpha) {
89  alpha *= half;
90  }
91  else {
92  alpha = alpha1;
93  }
94  // Update iterate
95  xnew_->set(x); xnew_->axpy(alpha,s);
96  // Get objective value at xnew
98  fval = obj.value(*xnew_,tol);
99  ls_neval++;
100  }
101  }
102 }; // class ROL::CubicInterp_U
103 
104 } // namespace ROL
105 
106 #endif
Provides interface for and implements line searches.
virtual void initialize(const Vector< Real > &x, const Vector< Real > &g)
Provides the interface to evaluate objective functions.
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) override
virtual ROL::Ptr< Vector > clone() const =0
Clone to make a new (uninitialized) vector.
Ptr< Vector< Real > > xnew_
virtual bool status(const ELineSearchU type, int &ls_neval, int &ls_ngrad, const Real alpha, const Real fold, const Real sgold, const Real fnew, const Vector< Real > &x, const Vector< Real > &s, Objective< Real > &obj)
virtual Real value(const Vector< Real > &x, Real &tol)=0
Compute value.
CubicInterp_U(ParameterList &parlist)
Defines the linear algebra or vector space interface.
Definition: ROL_Vector.hpp:46
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)
virtual void update(const Vector< Real > &x, UpdateType type, int iter=-1)
Update objective function.
Implements cubic interpolation back tracking line search.
void initialize(const Vector< Real > &x, const Vector< Real > &g) override