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An Interior-Point Method for a Class of Saddle-Point Problems

Author

Listed:
  • B.V. Halldórsson

    (Informatics Research, Celera Genomics)

  • R.H. Tütüncü

    (Carnegie Mellon University)

Abstract

We present a polynomial-time interior-point algorithm for a class of nonlinear saddle-point problems that involve semidefiniteness constraints on matrix variables. These problems originate from robust optimization formulations of convex quadratic programming problems with uncertain input parameters. As an application of our approach, we discuss a robust formulation of the Markowitz portfolio selection model.

Suggested Citation

  • B.V. Halldórsson & R.H. Tütüncü, 2003. "An Interior-Point Method for a Class of Saddle-Point Problems," Journal of Optimization Theory and Applications, Springer, vol. 116(3), pages 559-590, March.
    • Handle: RePEc:spr:joptap:v:116:y:2003:i:3:d:10.1023_a:1023065319772
    DOI: 10.1023/A:1023065319772
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    References listed on IDEAS

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    1. Yu. E. Nesterov & M. J. Todd, 1997. "Self-Scaled Barriers and Interior-Point Methods for Convex Programming," Mathematics of Operations Research, INFORMS, vol. 22(1), pages 1-42, February.
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    Cited by:

    1. Lara Dalmeyer & Tim Gebbie, 2021. "Geometric insights into robust portfolio construction," Papers 2107.06194, arXiv.org, revised Jun 2022.
    2. Shashank Oberoi & Mohammed Bilal Girach & Siddhartha P. Chakrabarty, 2019. "Can robust optimization offer improved portfolio performance?: An empirical study of Indian market," Papers 1908.04962, arXiv.org.
    3. Jose Blanchet & Lin Chen & Xun Yu Zhou, 2022. "Distributionally Robust Mean-Variance Portfolio Selection with Wasserstein Distances," Management Science, INFORMS, vol. 68(9), pages 6382-6410, September.
    4. Thomas Schmelzer & Raphael Hauser, 2013. "Seven Sins in Portfolio Optimization," Papers 1310.3396, arXiv.org.
    5. Karthik Natarajan & Dessislava Pachamanova & Melvyn Sim, 2009. "Constructing Risk Measures from Uncertainty Sets," Operations Research, INFORMS, vol. 57(5), pages 1129-1141, October.
    6. Shashank Oberoi & Mohammed Bilal Girach & Siddhartha P. Chakrabarty, 2020. "Can Robust Optimization Offer Improved Portfolio Performance? An Empirical Study of Indian market," Journal of Quantitative Economics, Springer;The Indian Econometric Society (TIES), vol. 18(3), pages 611-630, September.
    7. Raphael Hauser & Vijay Krishnamurthy & Reha Tutuncu, 2013. "Relative Robust Portfolio Optimization," Papers 1305.0144, arXiv.org, revised May 2013.

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