Difference between revisions of "Lbfgs.m"
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| − | {{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 | ||
==Syntax== | ==Syntax== | ||
| − | direction=lbfgs(dx_hist,dg_hist,g | + | direction=lbfgs(dx_hist,dg_hist,g) |
| − | == | + | ==Parameters== |
| − | dx_hist - history of x increments, | + | dx_hist - history of x increments, a stack |
| − | + | of column vectors, from the latest | |
| + | to the earliest | ||
dg_hist - history of gradient increments, | dg_hist - history of gradient increments, | ||
| − | + | a stack of column vectors, from | |
| + | the latest to the earliest | ||
g - current gradient | g - current gradient | ||
| − | |||
| − | |||
| − | |||
| − | == | + | ==Output== |
direction - LBFGS approximation to the | direction - LBFGS approximation to the | ||
| Line 25: | Line 24: | ||
==Notes== | ==Notes== | ||
| − | The L-BFGS algorithm is the default of [[ | + | The L-BFGS algorithm is the default of [[Fmaxnewton.m]], and is a good mix of computational efficiency and fast convergence. |
==See also== | ==See also== | ||
| − | [[ | + | [[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
