A modified exact Jacobian semidefinite programming(SDP)relaxation method is proposed in this paper to solve the Celis-Dennis-Tapia(CDT)problem using the Jacobian matrix of objective and constraining polynomials.In the...A modified exact Jacobian semidefinite programming(SDP)relaxation method is proposed in this paper to solve the Celis-Dennis-Tapia(CDT)problem using the Jacobian matrix of objective and constraining polynomials.In the modified relaxation problem,the number of introduced constraints and the lowest relaxation order decreases significantly.At the same time,the finite convergence property is guaranteed.In addition,the proposed method can be applied to the quadratically constrained problem with two quadratic constraints.Moreover,the efficiency of the proposed method is verified by numerical experiments.展开更多
基金Fundamental Research Funds for the Central Universities,China(No.2232019D3-38)Shanghai Sailing Program,China(No.22YF1400900)。
文摘A modified exact Jacobian semidefinite programming(SDP)relaxation method is proposed in this paper to solve the Celis-Dennis-Tapia(CDT)problem using the Jacobian matrix of objective and constraining polynomials.In the modified relaxation problem,the number of introduced constraints and the lowest relaxation order decreases significantly.At the same time,the finite convergence property is guaranteed.In addition,the proposed method can be applied to the quadratically constrained problem with two quadratic constraints.Moreover,the efficiency of the proposed method is verified by numerical experiments.
