Journal of Jishou University(Natural Sciences Edition)

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Numerical Methods for Vector Polynomial Optimization Problem

PENG Xueke, ZHOU Guangming, ZHAO Wenjie   

  1. (School of Mathematics and Computational Science, Xiangtan University, Xiangtan 411105, Hunan China)
  • Online:2019-07-25 Published:2019-07-31


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.

Key words: vector polynomial optimization, polynomial optimization, objective function, constraint condition, weak efficient solution

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