On Uniqueness of Lagrange Multipliers in Optimization Problems Subject to Cone Constraints

In this paper we study uniqueness of Lagrange multipliers in optimization problems subject to cone constraints. The main tool in our investigation of this question will be a calculus of dual (polar) cones. We give sufficient and in some cases necessary conditions for uniqueness of Lagrange multipliers in general Banach spaces. General results arethen applied to two particular examples of the semidefinite and semi-infinite programming problems, respectively.