QuantLib_ArmijoLineSearch man page

ArmijoLineSearch — Armijo line search.

Synopsis

#include <ql/math/optimization/armijo.hpp>

Inherits LineSearch.

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.

Additional Inherited Members

Detailed Description

Armijo line search.

Let $ alpha $ and $ beta $ be 2 scalars in $ [0,1] $. Let $ x $ be the current value of the unknown, $ d $ the search direction and $ t $ the step. Let $ f $ be the function to minimize. The line search stops when $ t $ verifies [ f(x + t cdot d) - f(x) leq -alpha t f'(x+t cdot d) ] and [ f(x+ac{t}{beta} cdot d) - f(x) > -ac{alpha}{beta} t f'(x+t cdot d) ]

(see Polak, Algorithms and consistent approximations, Optimization, volume 124 of Applied Mathematical Sciences, Springer-Verlag, NY, 1997)

Author

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Referenced By

ArmijoLineSearch(3) is an alias of QuantLib_ArmijoLineSearch(3).

Fri Sep 23 2016 Version 1.8.1 QuantLib