object

`bfgs(Problem)`

Problem - Problem object implementing local_optimization_problem_protocol and defining gradient/2.

BFGS (Broyden-Fletcher-Goldfarb-Shanno) dense quasi-Newton local optimizer with backtracking Armijo line search. Requires the problem to define gradient/2. Supports optional box constraints via projection, minimization and maximization.

Availability:

logtalk_load(local_optimization(loader))

Author: Paulo Moura
Version: 1:0:0
Date: 2026-09-03

Compilation flags:

static, context_switching_calls

Imports:

public local_optimization_solver(Problem)

Uses:

linear_algebra

list

Remarks:

Update: Maintains a dense approximation to the inverse Hessian, updated after every accepted step with the standard BFGS rank-two formula. The approximation starts at the identity matrix.

Internal minimization form: Maximization is handled by internally minimizing the negated objective and gradient; the quasi-Newton direction, curvature test, and Armijo condition are therefore always expressed in minimization form, which avoids sign errors in the line search.

Curvature safeguard: Whenever the curvature condition y . s > 0 is not comfortably satisfied (possible here since the line search only enforces sufficient decrease, not a Wolfe curvature condition), the inverse-Hessian approximation is reset to the identity matrix and the next step falls back to steepest descent, rather than keeping a stale approximation that would otherwise keep producing the same near-zero-progress direction.

Restarts: The restart(N) option (off by default) periodically resets the inverse-Hessian approximation to the identity matrix, exactly as conjugate_gradient(_) resets its search direction.

Bounds: When the problem defines position_bounds/1, trial points are projected onto the box after each step. Projection can weaken the quasi-Newton model; a pure bound-constrained formulation (L-BFGS-B style) is not implemented.