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The Rate of Convergence of a NLM Based on F–B NCP for Constrained Optimization Problems Without Strict Complementarity

Author

Listed:
  • Suxiang He

    (School of Science, Wuhan University of Technology, Wuhan 430070, P. R. China)

  • Liwei Zhang

    (School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, P. R. China)

  • Jie Zhang

    (School of Mathematics, Liaoning Normal University, Dalian 116029, P. R. China)

Abstract

It is well-known that the linear rate of convergence can be established for the classical augmented Lagrangian method for constrained optimization problems without strict complementarity. Whether this result is still valid for other nonlinear Lagrangian methods (NLM) is an interesting problem. This paper proposes a nonlinear Lagrangian function based on Fischer–Burmeister (F–B) nonlinear complimentarity problem (NCP) function for constrained optimization problems. The rate of convergence of this NLM is analyzed under the linear independent constraint qualification and the strong second-order sufficient condition without strict complementarity when subproblems are assumed to be solved exactly and inexactly, respectively. Interestingly, it is demonstrated that the Lagrange multipliers associating with inactive inequality constraints at the local minimum point converge to zeros superlinearly. Several illustrative examples are reported to show the behavior of the NLM.

Suggested Citation

  • Suxiang He & Liwei Zhang & Jie Zhang, 2015. "The Rate of Convergence of a NLM Based on F–B NCP for Constrained Optimization Problems Without Strict Complementarity," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 32(03), pages 1-27.
    • Handle: RePEc:wsi:apjorx:v:32:y:2015:i:03:n:s0217595915500128
    DOI: 10.1142/S0217595915500128
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