向量多项式优化问题的数值方法

向量多项式优化问题中的目标函数和约束条件都是由多项式描述的.先将多目标多项式函数分别通过主要目标法、线性加权和法和理想点法等转化为单目标多项式函数,再利用Lasserre松弛方法求解该多项式优化问题,从而得到原向量多项式优化问题的弱有效解或有效解.数值实验结果表明该数值方法是有效的.

Numerical Methods for Vector Polynomial Optimization Problem

For vector polynomial optimization problem, the objective function and constraint condition are all described in polynomial. Firstly, the multi-objective polynomial function is transformed into the single-objective polynomial function by using the main objective method, linear weighted sum method and ideal point method respectively. Then Lasserre relaxation method is applied to solve the polynomial optimization problem, and its optimal solution is obtained, which is also the weak efficient solution or effective solution of the original vector polynomial optimization problem. Numerical experiments show that the proposed numerical methods are effective.