- QuantLib
- ArmijoLineSearch
 
Armijo line search. More...
#include <ql/math/optimization/armijo.hpp>

| Public Member Functions | |
| ArmijoLineSearch (Real eps=1e-8, Real alpha=0.05, Real beta=0.65) | |
| Default constructor. | |
| Real | operator() (Problem &P, EndCriteria::Type &ecType, const EndCriteria &, const Real t_ini) | 
| Perform line search. | |
Armijo line search.
Let  and
 and  be 2 scalars in
 be 2 scalars in ![$ [0,1] $](form_221.png) . Let
. Let  be the current value of the unknown,
 be the current value of the unknown,  the search direction and
 the search direction and  the step. Let
 the step. Let  be the function to minimize. The line search stops when
 be the function to minimize. The line search stops when  verifies
 verifies 
![\[ f(x + t \cdot d) - f(x) \leq -\alpha t f'(x+t \cdot d) \]](form_223.png) 
and
![\[ f(x+\frac{t}{\beta} \cdot d) - f(x) > -\frac{\alpha}{\beta} t f'(x+t \cdot d) \]](form_224.png) 
(see Polak, Algorithms and consistent approximations, Optimization, volume 124 of Applied Mathematical Sciences, Springer-Verlag, NY, 1997)