Numerical solution of elliptic partial diffe rential equations and their optimal control problems

Abstract The mathematical theory of optimal control has emerged rapidly in the past few decades as an essential and independent field in applied mathematics. This theory not only has a profound theoretical foundation in the field of mathematics, but also shows strong application value in many practical application fields such as physical engineering, biological engineering and social science. In these problems, it is necessary to solve the minimization problem of a given cost function under satisfying differential equations and certain constraints. The optimal control problem studied in this paper is constrained by elliptic partial differential equations.