Comments on: Critical Lagrange multipliers: what we currently know about them, how they spoil our lives, and what we can do about it

Abstract

In these comments on the excellent survey paper by Izmailov and Solodov, we briefly discuss the main issues of critical Lagrange multipliers discovered and analyzed by the authors and then formulate some topics of interest for the future research. The latter topics concern the study of a possible influence of critical Lagrange multipliers on the convergence of primal–dual numerical algorithms of finding not general global and local minimizers but those satisfying certain desired stability properties known as tilt and full stability, which are briefly surveyed in these comments.