A penalty function method for solving weak price control problem
The authors are concerned with a class of weak price control problems, which is an important linear bilevel programming problem with non-unique lower level solutions. In order to explore the existence of an optimal solution, the weak price control problem is transformed into the corresponding penalized problem, which is a quadratic programming problem. Then the relationship between the solutions of the weak price control problem and the corresponding penalized problem is established. Based on the theoretical results a simple algorithm to solve the weak price control problem is given and the convergence of the proposed algorithm is analysed. A numerical example shows that the algorithm is feasible and efficient.
scientific article; zbMATH DE number 5162007