1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
|
// CppNumericalSolver
#ifndef ARMIJO_H_
#define ARMIJO_H_
#include "../meta.h"
namespace cppoptlib {
template<typename ProblemType, int Ord>
class Armijo {
public:
using Scalar = typename ProblemType::Scalar;
using TVector = typename ProblemType::TVector;
/**
* @brief use Armijo Rule for (weak) Wolfe conditiions
* @details [long description]
*
* @param searchDir search direction for next update step
* @param objFunc handle to problem
*
* @return step-width
*/
static Scalar linesearch(const TVector &x, const TVector &searchDir, ProblemType &objFunc, const Scalar alpha_init = 1.0) {
const Scalar c = 0.2;
const Scalar rho = 0.9;
Scalar alpha = alpha_init;
Scalar f = objFunc.value(x + alpha * searchDir);
const Scalar f_in = objFunc.value(x);
TVector grad(x.rows());
objFunc.gradient(x, grad);
const Scalar Cache = c * grad.dot(searchDir);
const Scalar alpha_min = 1e-8;
while(f > f_in + alpha * Cache && alpha > alpha_min) {
alpha *= rho;
f = objFunc.value(x + alpha * searchDir);
}
return alpha;
}
};
template<typename ProblemType>
class Armijo<ProblemType, 2> {
public:
using typename ProblemType::Scalar;
using typename ProblemType::TVector;
using typename ProblemType::THessian;
/**
* @brief use Armijo Rule for (weak) Wolfe conditiions
* @details [long description]
*
* @param searchDir search direction for next update step
* @param objFunc handle to problem
*
* @return step-width
*/
static Scalar linesearch(const TVector &x, const TVector &searchDir, ProblemType &objFunc) {
const Scalar c = 0.2;
const Scalar rho = 0.9;
Scalar alpha = 1.0;
Scalar f = objFunc.value(x + alpha * searchDir);
const Scalar f_in = objFunc.value(x);
const THessian hessian(x.rows(), x.rows());
objFunc.hessian(x, hessian);
TVector grad(x.rows());
objFunc.gradient(x, grad);
const Scalar Cache = c * grad.dot(searchDir) + 0.5 * c*c * searchDir.transpose() * (hessian * searchDir);
while(f > f_in + alpha * Cache) {
alpha *= rho;
f = objFunc.value(x + alpha * searchDir);
}
return alpha;
}
};
}
#endif /* ARMIJO_H_ */
|
