A mathematical programming problem with singular mixed pointwise-integral constraints

Maïtine Bergounioux (1) , Patrick Maheux (1)

1 MAPMO - Mathématiques - Analyse, Probabilités, Modélisation - Orléans

We investigate an infinite dimensional optimization problem which constraints are singular integral-pointwise ones. We give some partial results of existence for a solution in some particular cases. However, the lack of compactness, even in L1 prevents to conclude in the general case. We give an existence result for a weak solution (as a measure) that we are able to describe. The regularity of such a solution is still an open problem

Mots clés: Compactness; Measure; Minimization

Domaines: Optimisation et contrôle [math.OC]

Maïtine Bergounioux, Patrick Maheux. A mathematical programming problem with singular mixed pointwise-integral constraints. Journal of Mathematical Analysis and Applications, 2005, 308, n°2, pp 491-512. ⟨hal-00022003⟩