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论文类型：期刊论文

发表时间：2016-04-02

发表刊物：OPTIMIZATION

收录刊物：SCIE

卷号：65

期号：4

页面范围：729-749

ISSN号：0233-1934

关键字：nonlinear programming; spline function; homotopy method; interior-point method; 90C30; 49M37

摘要：Homotopy methods are globally convergent under weak conditions and robust; however, the efficiency of a homotopy method is closely related with the construction of the homotopy map and the path tracing algorithm. Different homotopies may behave very different in performance even though they are all theoretically convergent. In this paper, a spline smoothing homotopy method for nonconvex nonlinear programming is developed using cubic spline to smooth the max function of the constraints of nonlinear programming. Some properties of spline smoothing function are discussed and the global convergence of spline smoothing homotopy under the weak normal cone condition is proven. The spline smoothing technique uses a smooth constraint instead of m constraints and acts also as an active set technique. So the spline smoothing homotopy method is more efficient than previous homotopy methods like combined homotopy interior point method, aggregate constraint homotopy method and other probability one homotopy methods. Numerical tests with the comparisons to some other methods show that the new method is very efficient for nonlinear programming with large number of complicated constraints.