IDEAS home Printed from https://ideas.repec.org/p/cvh/coecwp/2024-04.html
   My bibliography  Save this paper

Parabolic Target-Space Interior-Point Algorithm for Weighted Monotone Linear Complementarity Problem

Author

Listed:
  • E. Nagy, Marianna
  • Illés, Tibor
  • Nesterov, Yurii
  • Rigó, Petra Renáta

Abstract

In this paper, we revisit the main principles for constructing polynomial-time primal-dual interior-point algorithms (IPAs). Starting from the break-through paper by Gonzaga (1989), their development was related to the barrier methods, where the objective function was added to the barrier for the feasible set. With this construction, using the theory of self-concordant functions proposed by Nesterov and Nemirovski (1994), it was possible to develop different variants of IPAs for a large variety of convex problems. However, in order to solve the initial problem, the most efficient primal-dual methods need to follow several central paths (up to three), which correspond to different stages of the solution process. This multistage structure of the methods significantly reduces their efficiency. In this paper, we come back to the initial idea by Renegar (1988) of using the methods of centers. We implement it for the weighted Linear Complementarity Problem (WLCP), by extending the framework of Parabolic Target Space (PTS), proposed by Nesterov (2008) for primal-dual Linear Programming Problems. This approach has several advantages. It starts from an arbitrary strictly feasible primal-dual pair and travels directly to the solution of the problem in one stage. It has the best known worst-case complexity bound. Finally, it works in a large neighborhood of the deviated central path, allowing very large steps. The latter ability results in a significant acceleration in the end of the process, confirmed by our preliminary computational experiments.

Suggested Citation

  • E. Nagy, Marianna & Illés, Tibor & Nesterov, Yurii & Rigó, Petra Renáta, 2024. "Parabolic Target-Space Interior-Point Algorithm for Weighted Monotone Linear Complementarity Problem," Corvinus Economics Working Papers (CEWP) 2024/04, Corvinus University of Budapest.
  • Handle: RePEc:cvh:coecwp:2024/04
    as

    Download full text from publisher

    File URL: https://unipub.lib.uni-corvinus.hu/10311/
    File Function: original version
    Download Restriction: no
    ---><---

    More about this item

    Keywords

    interior-point algorithm; parabolic target-space; monotone linear complementarity problems; bisymmetric matrices; polynomial complexity;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:cvh:coecwp:2024/04. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Adam Hoffmann (email available below). General contact details of provider: https://edirc.repec.org/data/bkeeehu.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.