The many faces of degeneracy in conic optimization

Understand

Slater's condition -- existence of a "strictly feasible solution" -- is a common assumption in conic optimization.

• Without strict feasibility, first-order optimality conditions may be meaningless, the dual problem may yield little information about the primal, and small changes in the data may render the problem infeasible.
• Hence, failure of strict feasibility can negatively impact off-the-shelf numerical methods, such as primal-dual interior point methods, in particular.
• New optimization modelling techniques and convex relaxations for hard nonconvex problems have shown that the loss of strict feasibility is a more pronounced phenomenon than has previously been realized.