Hiroshi Teramoto (Kansai University)

Title: Classification, recognition and bifurcation of feasible set germs

Abstract: Feasible set is the set of all possible points of an optimization problem that satisfy the problem's constraints including inequalities and equalities. In case of functions involving constraints are smooth, we classify constraints relative to K[G]-equivalence for a certain Lie group G. This classification provides the lists of constraints that can appear generically. Then, we classify feasible set germs defined by the constraints. The keys to the classification are tangent cones and contact types of corners of feasible set germs that involves a generalization of Montaldi's results on contact between submanifolds. In this talk, we also touch on recognition and bifurcation of feasible set germs. This is a joint work with Kenta Hayano (Keio University) and Naoki Hamada (KLab Ltd.).