Guignard’s Constraint Qualification (GCQ) and Multiobjective Optimisation Problems

Uncertain Constraint Optimisation Problems

Data uncertainties are inherent in the real world. The uncertain CSP (UCSP) is an extension of classical CSP that models incomplete and erroneous data by coefficients in the constraints whose values are unknown but bounded, for instance by an interval. It resolution is a closure, a set of potential solutions. This paper extends the UCSP model to account for optimisation criteria, by defining th...

Mixed Duality for Nonsmooth Multiobjective Fractional Programming without a Constraint Qualification

Interaction of Constraint Programming and Local Search for Optimisation Problems

In this paper we show, for the specific problem of test pattern optimisation, that adapting constraint propagation with results obtained from local search outperforms the use of each of these techniques alone. We show that a tool we developed to solve this problem using such approach with multivalued logics achieves better results than those obtained with a highly efficient tool based on an int...

Constraint qualification failure in action

This note presents a theoretical analysis of disjunctive constraints featuring unbounded variables. In this framework, classical modeling techniques, including big-M approaches, are not applicable. We introduce a lifted second-order cone formulation of such on/off constraints and discuss related constraint qualification issues. A solution is proposed to avoid solvers’ failure.

On constraint qualifications in directionally differentiable multiobjective optimization problems

We consider a multiobjective optimization problem with a feasible set defined by inequality and equality constraints such that all functions are, at least, Dini differentiable (in some cases, Hadamard differentiable and sometimes, quasiconvex). Several constraint qualifications are given in such a way that generalize both the qualifications introduced by Maeda and the classical ones, when the f...