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On the Complexity of a Column Generation Algorithm for Convex or Quasiconvex Feasibility Problems

In: Large Scale Optimization

Author

Listed:
  • Jean-Louis Goffin

    (McGill University, Faculty of Management)

  • Zhi-Quan Luo

    (McMaster University, Department of Electrical and Computer Engineering)

  • Yinyu Ye

    (The University of Iowa, Department of Management Sciences)

Abstract

We analyze the convergence and the complexity of a potential reduction column generation algorithm for solving general convex or quasiconvex feasibility problems defined by a separation oracle. The oracle is called at the analytic center of the set given by the intersection of the linear inequalities which are the previous answers of the oracle. We show that the algorithm converges in finite time and is in fact a fully polynomial approximation algorithm, provided that the feasible region has an nonempty interior. This result is based on the works of Ye [22] and Nesterov [16].

Suggested Citation

  • Jean-Louis Goffin & Zhi-Quan Luo & Yinyu Ye, 1994. "On the Complexity of a Column Generation Algorithm for Convex or Quasiconvex Feasibility Problems," Springer Books, in: W. W. Hager & D. W. Hearn & P. M. Pardalos (ed.), Large Scale Optimization, pages 182-191, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4613-3632-7_10
    DOI: 10.1007/978-1-4613-3632-7_10
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