A lagrange multiplier theorem for control problems with state constraints

Jean-Jacques Alibert (1) , Jean-Pierre Raymond (2)

1 IMATH - Institut de Mathématiques de Toulon - EA 2134
2 MIP - Mathématiques pour l'Industrie et la Physique

We prove an existence theorem of Lagrange multipliers for an abstract control problem in Banach spaces. This theorem may be applied to obtain optimality conditions for control problems governed by partial differential equations in the presence of pointwise state constraints.

Keywords: Optimal control; Optimality conditions; Lagrange multipliers in Banach spaces; Karush\-Kuhn\-Tucker type theorems; Inequality constraints in Banach spaces

Domains: Analysis of PDEs [math.AP]

Jean-Jacques Alibert, Jean-Pierre Raymond. A lagrange multiplier theorem for control problems with state constraints. Numerical Functional Analysis and Optimization, 1998, 19 (7-8), pp.51-73. ⟨hal-00993908⟩