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Worst-Case Iteration Bounds for Log Barrier Methods on Problems with Nonconvex Constraints

Author

Listed:
  • Oliver Hinder

    (Industrial Engineering, University of Pittsburgh, Pittsburgh, Pennsylvania 15260)

  • Yinyu Ye

    (Department of Management Science and Engineering, Stanford University, Stanford, California 94305)

Abstract

Interior point methods (IPMs) that handle nonconvex constraints such as IPOPT, KNITRO and LOQO have had enormous practical success. We consider IPMs in the setting where the objective and constraints are thrice differentiable, and have Lipschitz first and second derivatives on the feasible region. We provide an IPM that, starting from a strictly feasible point, finds a μ -approximate Fritz John point by solving O ( μ − 7 / 4 ) trust-region subproblems. For IPMs that handle nonlinear constraints, this result represents the first iteration bound with a polynomial dependence on 1 / μ . We also show how to use our method to find scaled-KKT points starting from an infeasible solution and improve on existing complexity bounds.

Suggested Citation

  • Oliver Hinder & Yinyu Ye, 2024. "Worst-Case Iteration Bounds for Log Barrier Methods on Problems with Nonconvex Constraints," Mathematics of Operations Research, INFORMS, vol. 49(4), pages 2402-2424, November.
    • Handle: RePEc:inm:ormoor:v:49:y:2024:i:4:p:2402-2424
    DOI: 10.1287/moor.2020.0274
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