Penalty Function Method For Optimization Problems With Switching Constraints Optimization

The switching-constrained optimization problem have important application prospects in modern economy and science and technology.In switching-constrained optimization problem,most of the existing algorithms cannot be directly applied to this problem because the common constraint specifications are not satisfied due to switching-constrained.For optimization problems with complex constraints,it is common to transform them into equationally constrained,unequally constrained or unconstrained optimization problems,and the penalty function approach is an important way to deal with such problems.In this thesis,we propose a partial penalty function approach for the optimization problem with switching-constrained by putting the difficult switching-constrained in the objective function.It is also shown that under the linearly independent constraint specification of the switching-constrained,the clustering point of the sequence of stable points of the partial penalty problem is the weakly stable point of the original problem.At the same time,there exists a sequence of local optimal solutions of the partial penalty problem that converges to any strictly local optimal solution of the original problem.The numerical results show that the method is feasible.Further,since the switching-constrained optimization problem has not only switching-constrained terms but also inequality and equation constraint terms,they are also difficult to solve so all the constraint terms are considered to be penalized to the objective function.Based on the external penalty function method of nonlinear programming,all the constraints of the switching-constrained optimization problem are penalized to the objective function to obtain an unconstrained optimization problem.It is also shown that under appropriate conditions,the optimal solution of the external penalty problem is the optimal solution of the original problem.At the same time,the iterative point column generated by the external penalty algorithm has the weakly stable points of the original problem.Finally,it is shown through numerical experiments that the external penalty function method is feasible.