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Long-step path-following algorithm for solving symmetric programming problems with nonlinear objective functions

Author

Listed:
  • Leonid Faybusovich

    (University of Notre Dame)

  • Cunlu Zhou

    (University of Notre Dame)

Abstract

We developed a long-step path-following algorithm for a class of symmetric programming problems with nonlinear convex objective functions. The theoretical framework is developed for functions compatible in the sense of Nesterov and Nemirovski with $$-\,\ln \det $$ - ln det barrier function. Complexity estimates similar to the case of a linear-quadratic objective function are established, which gives an upper bound for the total number of Newton steps. The theoretical scheme is implemented for a class of spectral objective functions which includes the case of quantum (von Neumann) entropy objective function, important from the point of view of applications. We explicitly compare our numerical results with the only known competitor.

Suggested Citation

  • Leonid Faybusovich & Cunlu Zhou, 2019. "Long-step path-following algorithm for solving symmetric programming problems with nonlinear objective functions," Computational Optimization and Applications, Springer, vol. 72(3), pages 769-795, April.
    • Handle: RePEc:spr:coopap:v:72:y:2019:i:3:d:10.1007_s10589-018-0054-7
    DOI: 10.1007/s10589-018-0054-7
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    References listed on IDEAS

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    1. Leonid Faybusovich, 2015. "On Hazan’s Algorithm for Symmetric Programming Problems," Journal of Optimization Theory and Applications, Springer, vol. 164(3), pages 915-932, March.
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    Cited by:

    1. Chee-Khian Sim, 2019. "Interior point method on semi-definite linear complementarity problems using the Nesterov–Todd (NT) search direction: polynomial complexity and local convergence," Computational Optimization and Applications, Springer, vol. 74(2), pages 583-621, November.
    2. Faybusovich, Leonid & Zhou, Cunlu, 2020. "Self-concordance and matrix monotonicity with applications to quantum entanglement problems," Applied Mathematics and Computation, Elsevier, vol. 375(C).

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