Indexed by:期刊论文

Date of Publication:2014-01-01

Journal:PACIFIC JOURNAL OF OPTIMIZATION

Included Journals:SCIE

Volume:10

Issue:1,SI

Page Number:37-51

ISSN No.:1348-9151

Key Words:spline function; homotopy method; nonlinear programming; global convergence

Abstract:In this paper, a constraint shifting spline smoothing homotopy method (CSSSH) is proposed for solving nonlinear programming with both equality and inequality constraints. The global convergence of CSSSH under fairly weak conditions is proven. All problems that can be solved by previous homotopy methods can also be solved by the proposed method. The CSSSH-S-N procedure is given. The spline smoothing technique uses a smooth inequality constraint instead of m inequality constraints. At each iteration, the smooth spline approximation of the max-function of the inequality constraints involves only few inequality constraints, hence the number of gradient and Hessian calculations is reduced dramatically, so the CSSSH is more efficient than previous homotopy methods like, combined homotopy interior point method(CHIP), combined homotopy infeasible interior point method (CHIIP) and constraint shifting homotopy method (CSH). And the starting point in the proposed method is not necessarily a feasible point or an interior point, so it is more convenient to be implemented than CHIP and CHIIP. Numerical tests with the comparisons to some other methods show that the new method is very efficient for nonlinear programming with both equality and large number of complicated inequality constraints.