Convergence of Exponential Penalty Function Method for Variational Problems

Abstract

In this paper, we propose an exponential penalty function method in order to solve a constrained variational problem by transforming it into a sequence of unconstrained ones. Further, we analyze the relationship between the optimal solutions of the sequence of exponential penalized variational problems and that of the original constrained variational problem. The convergence of this exponential penalty method is also examined for variational problems. Numerical examples are provided to verify the obtained results and validate the efficient use of exponential penalty method for solving constrained variational problems.