Why there is no need to use a big-M in linear bilevel optimization: A computational study of two ready-to-use approaches

Linear bilevel optimization problems have gained increasing attention both in theory as well as in practical applications of Operations Research (OR) during the last years and decades. The latter is mainly due to the ability of this class of problems to model hierarchical decision processes. However, this ability makes bilevel problems also very hard to … Read more

On the computation of convex envelopes for bivariate functions through KKT conditions

In this paper we exploit a slight variant of a result previously proved in [11] to define a procedure which delivers the convex envelope of some bivariate functions over polytopes. The procedure is based on the solution of a KKT system and simplifies the derivation of the convex envelope with respect to previously proposed techniques. … Read more

A cone-continuity constraint qualification and algorithmic consequences

Every local minimizer of a smooth constrained optimization problem satisfies the sequential Approximate Karush-Kuhn-Tucker (AKKT) condition. This optimality condition is used to define the stopping criteria of many practical nonlinear programming algorithms. It is natural to ask for conditions on the constraints under which AKKT implies KKT. These conditions will be called Strict Constraint Qualifications … Read more

Constant rank constraint qualifications: a geometric introduction

Constraint qualifications (CQ) are assumptions on the algebraic description of the feasible set of an optimization problem that ensure that the KKT conditions hold at any local minimum. In this work we show that constraint qualifications based on the notion of constant rank can be understood as assumptions that ensure that the polar of the … Read more