Optimal control of a parabolic equation with time-dependent state constraints

In this paper we study the optimal control problem of the heat equation by a distributed control over a subset of the domain, in the presence of a state constraint. The latter is integral over the space and has to be satisfied at each time. Using for the first time the technique of alternative optimality … Read more

Second-order analysis of optimal control problems with control and initial-final state constraints

This paper provides an analysis of Pontryagine mimina satisfying a quadratic growth condition, for optimal control problems of ordinary differential equations with constraints on initial-final state, as well as control constraints satisfying the uniform positive linear independence condition. Citation Rapport de Recherche INRIA 6707, Oct. 2008. Article Download View Second-order analysis of optimal control problems … Read more

Transposition theorems and qualification-free optimality conditions

New theorems of the alternative for polynomial constraints (based on the Positivstellensatz from real algebraic geometry) and for linear constraints (generalizing the transposition theorems of Motzkin and Tucker) are proved. Based on these, two Karush-John optimality conditions — holding without any constraint qualification — are proved for single- or multi-objective constrained optimization problems. The first … Read more