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

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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.

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Authors and Affiliations

  1. Department of Mathematical Sciences, Clemson University, Clemson, South Carolina

    X. B. Chen (PhD Student)

  2. Department of Mathematical Sciences, Clemson University, Clemson, South Carolina

    M. M. Kostreva (Professor)

Authors
  1. X. B. Chen
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  2. M. M. Kostreva
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Chen, X.B., Kostreva, M.M. Global Convergence Analysis of Algorithms for Finding Feasible Points in Norm-Relaxed MFD. Journal of Optimization Theory and Applications 100, 287–309 (1999). https://doi.org/10.1023/A:1021778002066

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  • DOI: https://doi.org/10.1023/A:1021778002066

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