An Efficient Algorithm for Large-Scale Nonlinear Programming Problems with Simple Bounds on the Variables

Preconditioned conjugate gradient algorithms for nonconvex problems with box constraints

“…Although, as reported in [27], in terms of CPU time it is competitive to the benchmark L-BFGS-B code, in general it requires more function evaluations to find a stationary point. This paper introduces its preconditioned version which outperforms L-BFGS-B with respect to the number of function evaluations.…”

“…Both algorithms treat the box constraints similarly. They can be regarded as an extension of the algorithm introduced by Bertsekas in [3] and the conjugate gradient algorithm proposed in [27].…”

“…The conjugate gradient algorithm analyzed in [27] does not apply any preconditioner in defining the direction of descent. Although, as reported in [27], in terms of CPU time it is competitive to the benchmark L-BFGS-B code, in general it requires more function evaluations to find a stationary point.…”

“…In Sect. 2 we present the preconditioned version of the conjugate gradient which can be regarded as an extension of the algorithm stated in [27] obtained by incorporating preconditioning introduced in [28]. The convergence analysis discussed in Sect.…”

Numerical methods for large-scale nonlinear optimization

“…It is also unsurprising that, just as in the unconstrained case, there is no need for the objective function to decrease monotonically so long as there is some overall monotonic trend (Facchinei et al, 1998. Efforts have also been made to embed nonlinear CG methods within a gradient-projection framework (Pytlak, 1998). Filter ideas have also been investigated ) that use penalty techniques (see §5) to handle the bounds.…”