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

Abstract

The invited discussion paper, Critical Lagrange Multipliers: what we currently know about them, how they spoil our lives, and what we can do about it, written by Izmailov and Solodov is a clear and concise overview of dual stabilization methods for solving problems of the form minimize x∈Rn f (x) subject to h(x) = 0, (1) where the objective function f and constraint function h are assumed to be twicecontinuously differentiable. They focus on the equality constrained problem (1) so that key concepts can be clearly explained, but most of the discussion and many of the results have been extended to problems with inequality constraints. As the title suggests, emphasis is placed on critical Lagrange multipliers and the challenges that they introduce for designing efficient and robust algorithms for solving (1).