Operations Research Transactions ›› 2013, Vol. 17 ›› Issue (2): 89-106.

• Original Articles • Previous Articles     Next Articles

Affine scaling interior Levenberg-Marquardt method for KKT systems

WANG Yunjuan1,*,ZHU Detong2   

  1. 1. School of Mathematics and Information, Shanghai Lixin University of Commerce, Shanghai 201620, China 2. Business School, Shanghai Normal University, Shanghai 200234, China
  • Received:2011-03-24 Online:2013-06-15 Published:2013-06-15

Abstract: We develop and analyze a new affine scaling Levenberg-Marquardt method with nonmonotonic interior backtracking line search technique for solving Karush-Kuhn-Tucker (KKT) system. By transforming the KKT system into an equivalent minimization problem with nonnegativity constraints on some of the variables, we establish the Levenberg-Marquardt equation based on this reformulation. Theoretical analysis are given which prove that the proposed algorithm is globally convergent and has a local superlinear convergent rate under some reasonable conditions. The results of numerical experiments are reported to show the effectiveness of the proposed algorithm.

Key words: KKT systems, Levenberg-Marquardt method, affine scaling, interior point, convergence

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