Smoothing methods for mathematical programs with complementarity constraints

Computational methods for optimal control are for dealing with bottlenecks in industries. By implementing optimal operation strategies that are obtained form the important computational methods into dynamic systems, objectives such as saving energy, reducing cost, exploiting protential, improving efficiency can be achieved. In this paper, to conquer the difficulties that arise from inequality path constraints, the smooth approximation functions are studied, and the smoothed penalty function methods are proposed. The validities and convergencies of these smoothed penalty function methods are proved rigorously. Results from one case study indicate the capability of the proposed approaches to efficiently obtain physically meaningful solutions.