CAJ | 학술논문

本文研究了一类非线性不等式组的求解问题.利用一列目标函数两次可微的参数优化问题来逼近非线性不等式组的解,光滑Levenberg-Marquardt方法来求解参数优化问题,在一些较弱的条件下证明了文中算法的全局收敛性,数值实例显示文中算法效果较好.
본문연구료일류비선성불등식조적구해문제.이용일렬목표함수량차가미적삼수우화문제래핍근비선성불등식조적해,광활Levenberg-Marquardt방법래구해삼수우화문제,재일사교약적조건하증명료문중산법적전국수렴성,수치실례현시문중산법효과교호.
In this article,we study the solutions for a class of nonlinear inequalities.The nonlinear inequalities are approximated by a family of parameterized optimization problems with twice continuously differentiable objective functions,then a smoothing Levenberg-Marquardt method is applied to solve the parameterized optimization problems.The global convergence of the proposed method is established under some weak conditions.Numerical results show that the method performs well.