Abstract:
Strict feasibility is at the heart of convex optimization. This is
needed for optimality conditions, stability, and algorithmic
development. New optimization modelling techniques and convex
relaxations for hard nonconvex problems have shown that the loss of
strict feasibility is a much more pronounced phenomenon than previously
realized. These new developments suggest a reappraisal. We describe the
various reasons for the loss of strict feasibility, whether due to poor
modelling choices or (more interestingly) rich underlying structure, and
describe ways to cope with it and, in particular, "take advantage of
it".