Derivative-enhanced lower-Bounding in adaptive discretization for the global solution of semi-infinite optimization problems

Optimization, vol. 75, pp. 2667–2700

Abstract

We investigate the use of derivative information in the lower-bounding of adaptive discretization algorithms for semi-infinite optimization problems with linear constraints at the lower level. We propose a new discretization-based relaxation, enhanced with a convex restriction of the lower level and utilizing the first- and bounds for the second-order derivative of the semi-infinite constraint. The resulting subproblem maintains several advantageous characteristics from the original problem. By adaptively subdividing the lower-level feasible region, the subproblem is further refined. The resulting algorithm is shown to be superlinearly convergent (either locally or with respect to the width of relevant refined boxes) under suitable assumptions when the Hessian of the semi-infinite constraint is independent of the upper-level variables. We compare our proposed relaxation against existing lower-bounding approaches based on derivative information and adaptive discretization and show that excessive numbers of discretization points can be avoided.

Authors 2

1. Aron Zingler Aachen

   RWTH Aachen University

   Affiliation as printed

   RWTH Aachen University

2. Alexander Mitsos corresponding Aachen

   RWTH Aachen University · Forschungszentrum Jülich

   Affiliation as printed

   Forschungszentrum Jülich GmbH

   JARA-CSD

   RWTH Aachen University