A branch-and-bound algorithm for the computation of optimal point mappings of parametric optimization problems

We propose a novel branch‑and‑bound algorithm that constructs rigorous outer approximations of the optimal point mapping for parametric optimization problems with guaranteed feasibility and optimality tolerances. The method uses the improvement‑function reformulation to define discarding and inclusion tests on sub-boxes, constructing a rigorous outer approximation. Under the same regularity conditions that ensure exactness of this … Read more

The improvement function reformulation for graphs of minimal point mappings

Graphs of minimal point mappings of parametric optimization problems appear in the definition of feasible sets of bilevel optimization problems and of semi-infinite optimization problems, and the intersection of multiple such graphs defines (generalized) Nash equilibria. This paper shows how minimal point graphs of nonconvex parametric optimization problems can be written with the help of … Read more