CAJ | 학술논문

本文提出了一个求解非凸半定规划的非线性Lagrange算法,当二阶充分条件以及严格互补条件成立时,证明了这一算法的收敛性定理.收敛结果表明,当惩罚参数小于某个阀值时,算法是局部收敛的;此外,还给出了解的一个依赖于惩罚参数的误差界.
본문제출료일개구해비철반정규화적비선성Lagrange산법,당이계충분조건이급엄격호보조건성립시,증명료저일산법적수렴성정리.수렴결과표명,당징벌삼수소우모개벌치시,산법시국부수렴적;차외,환급출료해적일개의뢰우징벌삼수적오차계.
This paper proposes a nonlinear Lagrange algorithm for solving nonconvex semidefinite programming.Under the second order sufficient condition and the strict complementarity condition,the convergence theorem is established.The convergence theorem shows that the nonlinear Lagrange algorithm is locally convergent when the penalty parameter is smaller than a threshold.The error bound of solution,depending on the penalty parameter,is also given.