Difference between revisions of "Lbfgs.m"
(→See also) |
(Update function See also links and function index membership) |
||
| (4 intermediate revisions by the same user not shown) | |||
| Line 1: | Line 1: | ||
| − | {{DISPLAYTITLE:lbfgs.m}} | + | {{DISPLAYTITLE:lbfgs.m}} __NOTOC__ |
Calculates an approximation to the Newton-Raphson search direction using past gradients to build a serviceable substitute to a Hessian. The Hessian matrix is never explicitly formed or inverted. This function is the implementation from section 4 of http://dx.doi.org/10.1090/S0025-5718-1980-0572855-7 | Calculates an approximation to the Newton-Raphson search direction using past gradients to build a serviceable substitute to a Hessian. The Hessian matrix is never explicitly formed or inverted. This function is the implementation from section 4 of http://dx.doi.org/10.1090/S0025-5718-1980-0572855-7 | ||
| Line 6: | Line 6: | ||
direction=lbfgs(dx_hist,dg_hist,g) | direction=lbfgs(dx_hist,dg_hist,g) | ||
| − | == | + | ==Parameters== |
dx_hist - history of x increments, a stack | dx_hist - history of x increments, a stack | ||
| Line 15: | Line 15: | ||
a stack of column vectors, from | a stack of column vectors, from | ||
the latest to the earliest | the latest to the earliest | ||
| − | + | ||
g - current gradient | g - current gradient | ||
| Line 27: | Line 27: | ||
==See also== | ==See also== | ||
| − | [[fmaxnewton.m]], [[hessreg.m]], [[ | + | [[fmaxnewton.m]], [[hessreg.m]], [[bracketing.m]], [[sectioning.m]], [[bfgs_upd.m]], [[Optimal_control_module]] |
''Version 2.2, authors: [[Ilya Kuprov]], [[David Goodwin]]'' | ''Version 2.2, authors: [[Ilya Kuprov]], [[David Goodwin]]'' | ||
Latest revision as of 19:38, 6 June 2026
Calculates an approximation to the Newton-Raphson search direction using past gradients to build a serviceable substitute to a Hessian. The Hessian matrix is never explicitly formed or inverted. This function is the implementation from section 4 of http://dx.doi.org/10.1090/S0025-5718-1980-0572855-7
Syntax
direction=lbfgs(dx_hist,dg_hist,g)
Parameters
dx_hist - history of x increments, a stack
of column vectors, from the latest
to the earliest
dg_hist - history of gradient increments,
a stack of column vectors, from
the latest to the earliest
g - current gradient
Output
direction - LBFGS approximation to the
search direction
Notes
The L-BFGS algorithm is the default of Fmaxnewton.m, and is a good mix of computational efficiency and fast convergence.
See also
fmaxnewton.m, hessreg.m, bracketing.m, sectioning.m, bfgs_upd.m, Optimal_control_module
Version 2.2, authors: Ilya Kuprov, David Goodwin
