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Global Convergence Analysis of Algorithms for Finding Feasible Points in Norm-Relaxed MFD

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  • X. B. Chen

    (Clemson University)

  • M. M. Kostreva

    (Clemson University)

Abstract

This paper introduces two new algorithms for finding initial feasible points from initial infeasible points for the recently developed norm-relaxed method of feasible directions (MFD). Their global convergence is analyzed. The theoretical results show that both methods are globally convergent; one of them guarantees finding a feasible point in a finite number of steps. These two methods are very convenient to implement in the norm-relaxed MFD. Numerical experiments are carried out to demonstrate their performance on some classical test problems and to compare them with the traditional method of phase I problems. The numerical results show that the methods proposed in this paper are more effective than the method of phase I problems in the norm-relaxed MFD. Hence, they can be used for finding initial feasible points for other MFD algorithms and other nonlinear programming methods.

Suggested Citation

  • X. B. Chen & M. M. Kostreva, 1999. "Global Convergence Analysis of Algorithms for Finding Feasible Points in Norm-Relaxed MFD," Journal of Optimization Theory and Applications, Springer, vol. 100(2), pages 287-309, February.
    • Handle: RePEc:spr:joptap:v:100:y:1999:i:2:d:10.1023_a:1021778002066
    DOI: 10.1023/A:1021778002066
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    References listed on IDEAS

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    1. J. Korycki & M. Kostreva, 1997. "Self-Tuning Norm-Relaxed Method of Feasible Directions," Journal of Optimization Theory and Applications, Springer, vol. 92(2), pages 311-330, February.
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    Cited by:

    1. Wang, Jian & He, Xiaozheng & Peeta, Srinivas & Wang, Wei, 2022. "Globally convergent line search algorithm with Euler-based step size-determination method for continuous network design problem," Transportation Research Part B: Methodological, Elsevier, vol. 163(C), pages 119-144.

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