Abstract:

To find multiple optimal solutions and even the optimal solution set to the mathematical programming problem is a significant work both in theory and practice because the specific optimal plan that is most desirable can be selected by the decision maker. However, the study on finding multiple optimal solutions to the nonlinear programming problem for now is seldom seen and has limitations. The quadratic programming problem with the pseudoconvex objective function is considered. Firstly, the characteristic of the optimal solution set is presented and proved. Then, by the approach of finding all optimal solutions to an auxiliary linear programming with artificial variables, a condition for the unique optimal solution to the pseudoconvex quadratic programming is presented, and in the case that the condition is not sattisfied, the optimal solution set to the pseudoconvex quadratic programming is obtained by means of finding the optimal solution set to the auxiliary linear programming. Finally, two computational examples are also given to illustrate the effectiveness of the method.