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An Inexact Interior-Point Lagrangian Decomposition Algorithm with Inexact Oracles

Author

Listed:
  • Deyi Liu

    (The University of North Carolina at Chapel Hill)

  • Quoc Tran-Dinh

    (The University of North Carolina at Chapel Hill)

Abstract

We combine the Lagrangian dual decomposition, barrier smoothing, path-following, and proximal Newton techniques to develop a new inexact interior-point Lagrangian decomposition method to solve a broad class of constrained composite convex optimization problems. Our method allows one to approximately solve the primal subproblems (called the slave problems), which leads to inexact oracles (i.e., inexact function value, gradient, and Hessian) of the smoothed dual problem (called the master problem). By appropriately controlling the inexact computation in both the slave and master problems, we can still establish a polynomial-time iteration complexity of our algorithm and recover primal solutions. We illustrate the performance of our method through two numerical examples and compare it with existing methods.

Suggested Citation

  • Deyi Liu & Quoc Tran-Dinh, 2020. "An Inexact Interior-Point Lagrangian Decomposition Algorithm with Inexact Oracles," Journal of Optimization Theory and Applications, Springer, vol. 185(3), pages 903-926, June.
    • Handle: RePEc:spr:joptap:v:185:y:2020:i:3:d:10.1007_s10957-020-01680-3
    DOI: 10.1007/s10957-020-01680-3
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    References listed on IDEAS

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    1. Quoc Tran-Dinh & Anastasios Kyrillidis & Volkan Cevher, 2018. "A Single-Phase, Proximal Path-Following Framework," Mathematics of Operations Research, INFORMS, vol. 43(4), pages 1326-1347, November.
    2. NESTEROV, Yurii, 2013. "Gradient methods for minimizing composite functions," LIDAM Reprints CORE 2510, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    3. I. Necoara & J. A. K. Suykens, 2009. "Interior-Point Lagrangian Decomposition Method for Separable Convex Optimization," Journal of Optimization Theory and Applications, Springer, vol. 143(3), pages 567-588, December.
    4. John R. Birge, 1985. "Decomposition and Partitioning Methods for Multistage Stochastic Linear Programs," Operations Research, INFORMS, vol. 33(5), pages 989-1007, October.
    5. NESTEROV, Yurii, 2011. "Barrier subgradient method," LIDAM Reprints CORE 2359, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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