Differential inclusions and exact penalties

Abstract

The article considers differential inclusion with a given set-valued mapping and initial point. It is required to find a solution of this differential inclusion that minimizes an integral functional. Some classical results about the maximum principle for differential inclusions are obtained using the support and exact penalty functions. This is done for differentiable and for non-differentiable set-valued mappings in phase variables.

Keywords

• Nonsmooth functional
• differential inclusion
• support function
• exact penalty function
• maximum principle