A novel global optimization method to solve nonlinear programming problem with bounded variables

作者：Jin Xia; Duan Fuhai^*; Jiang Xiuhong

来源：Journal of Shanghai Jiaotong University, 2016, 50(6): 861-867.

DOI：10.16183/j.cnki.jsjtu.2016.06.008

• Computational process
• Feasible regions
• Global optimization method
• Linear inequality constraints
• Non-linear constraints
• Nonlinear programming problem
• Optimization problems
• Sequential quadratic programming

A novel global optimization method, increasingly removing infeasible region (IRIR), to solve the nonlinear programming problem with bounded variables, was presented. In the IRIR, the original infeasible regions were computed and removed from the original solution space, and the updated solution space was gradually reduced. The infeasible regions were expressed by linear inequalities so that the original nonlinear constraints were transformed into linear inequality constraints, and the nonlinear programming problem could be solved in the premise that the optimum design point was not excluded from the updated solution space. The characteristic of the IRIR is that the optimum obtained is insensitive to the starting point and the convexities of constraint functions. The principle and computational process of the IRIR were elaborated. Based on the sequential quadratic programming (SQP) algorithm, the application of the IRIR to two optimization problems, a numerical test problem and a spring design problem, illustrates the feasibility and correctness of the IRIR. The optimization results show that the IRIR can effectively lower the difficulty of solving the nonlinear programming problem. Besides, it is not necessary to introduce the additional parameter. The IRIR is a novel global optimization method with a high applicability and practicality. But, it is not applicable to problems with unbounded variables.

• 出版日期2016