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Modified Exact Jacobian Semidefinite Programming Relaxation for Celis-Dennis-Tapia Problem
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作者 赵馨 孔汕汕 《Journal of Donghua University(English Edition)》 CAS 2023年第1期96-104,共9页
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
关键词 celis-dennis-tapia(cdt)problem quadratically constrained problem with two quadratic constraints semidefinite programming(SDP)relaxation method
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一类扩展的CDT问题存在对偶间隙的充要条件
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作者 曲衍明 《软件》 2019年第4期124-127,共4页
在这篇文章中,作者研究一类带有两个二次约束的CDT问题,其中一个是单位球约束,一个是椭球约束。选取合适的通过最优线段的超平面,在不分割可行域的情况下,通过二阶锥重塑技术和半正定松弛的方法,得到了该CDT问题的二阶锥重塑问题存在对... 在这篇文章中,作者研究一类带有两个二次约束的CDT问题,其中一个是单位球约束,一个是椭球约束。选取合适的通过最优线段的超平面,在不分割可行域的情况下,通过二阶锥重塑技术和半正定松弛的方法,得到了该CDT问题的二阶锥重塑问题存在对偶间隙的充要条件,并给出了理论证明,为以后缩小甚至消除CDT问题的对偶间隙做铺垫。 展开更多
关键词 二次约束二次优化 cdt问题 二阶锥 半正定松弛
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Subspace choices for the Celis-Dennis-Tapia problem
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作者 ZHAO Xin FAN JinYan 《Science China Mathematics》 SCIE CSCD 2017年第9期1717-1732,共16页
Grapiglia et al.(2013) proved subspace properties for the Celis-Dennis-Tapia(CDT) problem. If a subspace with lower dimension is appropriately chosen to satisfy subspace properties, then one can solve the CDT problem ... Grapiglia et al.(2013) proved subspace properties for the Celis-Dennis-Tapia(CDT) problem. If a subspace with lower dimension is appropriately chosen to satisfy subspace properties, then one can solve the CDT problem in that subspace so that the computational cost can be reduced. We show how to find subspaces that satisfy subspace properties for the CDT problem, by using the eigendecomposition of the Hessian matrix of the objection function. The dimensions of the subspaces are investigated. We also apply the subspace technologies to the trust region subproblem and the quadratic optimization with two quadratic constraints. 展开更多
关键词 cdt problems subspace properties subspace choices
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