object

`trust_region_newton_cg(Problem)`

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

Trust-region Newton-CG local optimizer (Steihaug-CG for the subproblem). Requires the problem to define gradient/2 and hessian/2. Supports optional box constraints via projection, minimization and maximization.

Availability:

logtalk_load(local_optimization(loader))

Author: Paulo Moura
Version: 1:0:0
Date: 2026-08-24

Compilation flags:

static, context_switching_calls

Imports:

public local_optimization_solver(Problem)

Uses:

linear_algebra

list

Remarks:

Subproblem: At each outer iteration, the step is obtained by approximately minimizing the local quadratic model within a ball of radius trust_radius, using the Steihaug-CG method (Nocedal and Wright, Algorithm 7.2): plain conjugate gradient on the model, terminated early either by a negative-curvature direction or by reaching the trust-region boundary, in which case the step is extended to the boundary along the current CG direction.

No line search: Unlike the other gradient-based solvers in this library, this solver never backtracks a step size; the trust-region radius itself is grown or shrunk each iteration based on how well the quadratic model predicted the actual objective change, and a step is accepted only when that agreement is good enough.

Internal minimization form: Maximization is handled by internally minimizing the negated objective, gradient, and Hessian, so the subproblem and acceptance test are always expressed in minimization form, which avoids sign errors.

Convergence: Because it uses exact second-order information, this solver typically converges in far fewer iterations than gradient_descent(_), bfgs(_), or lbfgs(_) on well-behaved problems, at the cost of requiring an explicit hessian/2.

Bounds: When the problem defines position_bounds/1, trial points are projected onto the box after each step. Projection can weaken the trust-region model agreement (the accepted step may differ from the one the subproblem solved for), which can trigger more radius shrinkage than an unconstrained problem would; a pure bound-constrained formulation is not implemented.