LBFGSB

The L-BFGS-B (Limited-memory BFGS with Bound constraints) algorithm is a gradient-based optimization algorithm. This solver uses the ‘L-BFGS-B’ algorithm from the Scipy library.

Note

L-BFGS-B is a quasi-Newton optimization algorithm for large-scale bound-constrained problems. Therefore, it does not support other types of constraints. Please use general nonlinear programming algorithms like PySLSQP or IPOPT, if your problem has constraints other than optimization variable bounds.

To use the LBFGSB solver, start by importing it as shown in the following code:

from modopt import LBFGSB

Options could be set by just passing them within the solver_options dictionary when instantiating the LBFGSB optimizer object. For example, we can set the maximum number of iterations maxiter and the tolerance on the projected gradient gtol as shown below.

optimizer = LBFGSB(prob, solver_options={'maxiter':1000, 'gtol':1e-6})

The options available for the LBFGSB solver in modOpt are given in the following table. For more information on the Scipy ‘L-BFGS-B’ algorithm, visit Scipy documentation.

LBFGSB solver options
Option	Type (default value)	Description
`maxfun`	int (`1000`)	Maximum number of function (objective) evaluations.
`maxiter`	int (`200`)	Maximum number of iterations.
`maxls`	int (`20`)	Maximum number of line search steps per major iteration.
`maxcor`	int (`10`)	Maximum number of variable metric corrections used to define the limited memory Hessian approximation. LBFGSB does not store the full Hessian but uses this many terms to construct an approximation when required.
`ftol`	float (`2.22e-9`)	Terminate successfully if: `(f^k - f^{k+1})/max{\|f^k\|,\|f^{k+1}\|,1} <= ftol`
`gtol`	float(`1e-5`)	Terminate successfully if: `max{\|proj g_i \| i = 1, ..., n} <= gtol`, where `proj g_i` is the i-th component of the projected gradient.
`iprint`	int (`-1`)	Verbosity of the console output. < 0 suppresses all console outputs. = 0 prints a short summary upon completion. 0<iprint<99 also prints `f^k` and `\|proj g^k\|` at every iprint-th iteration. = 99 also prints more scalar variables at each iteration. = 100 also prints more Cauchy search data, changes in the active set and final `x`. > 100 also prints vectors `x`, `g`, and Cauchy `x` at every iteration.
`callback`	callable (`None`)	Function to be called after each major iteration. The function is called as`callback(xk, fk)`, where `xk` is the optimization variable vector from the current major iteration, and `fk` is the corresponding objective value.