ABSTRACT
We propose and analyze dynamic linear programming problem solvers. We use a penalty function method and variable structure systems approach to solve linear programming problems. We introduce a family of penalty functions which allows us to transform linear programming problems into unconstrained optimization problems. Bounds on the weight parameters of the penalty functions are derived, using a method from variable structure systems theory, for which the given linear program and the associated unconstrained optimization problem have the same solution. In addition, we have combined gradient projection and the penalty function methods for solving linear programming problems. Bounds on the weight parameters of the penalty functions for this method resulting in the exact solution are also given. Both proposed methods for solving linear programming problems can be interpreted from the variable structure systems viewpoint. Simulation examples are given to illustrate the results obtained.
