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Full Nesterov-Todd step feasible interior-point algorithm for symmetric cone horizontal linear complementarity problem based on a positive-asymptotic barrier function

Asadi, S ; Sharif University of Technology | 2022

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  1. Type of Document: Article
  2. DOI: 10.1080/10556788.2020.1734803
  3. Publisher: Taylor and Francis Ltd , 2022
  4. Abstract:
  5. We present a feasible full step interior-point algorithm to solve the (Formula presented.) horizontal linear complementarity problem defined on a Cartesian product of symmetric cones, which is not based on a usual barrier function. The full steps are scaled utilizing the Nesterov-Todd (NT) scaling point. Our approach generates the search directions leading to the full-NT steps by algebraically transforming the centring equation of the system which defines the central trajectory using the induced barrier of a so-called positive-asymptotic kernel function. We establish the global convergence as well as a local quadratic rate of convergence of our proposed method. Finally, we demonstrate that our algorithm bears a complexity bound matching the best available one for the algorithms of its kind. © 2020 Informa UK Limited, trading as Taylor & Francis Group
  6. Keywords:
  7. Cartesian symmetric cone horizontal linear complementarity problem ; Euclidean Jordan algebra ; Nesterov-Todd directions ; Linear transformations ; Algebraic transformation of the central path ; Algebraic transformations ; Asymptotics ; Barriers functions ; Cartesians ; Linear complementarity problems ; Nesterov-todd direction ; Positive-asymptotic barrier function ; Symmetric cone ; Computational complexity
  8. Source: Optimization Methods and Software ; Volume 37, Issue 1 , 2022 , Pages 192-213 ; 10556788 (ISSN)
  9. URL: https://www.tandfonline.com/doi/abs/10.1080/10556788.2020.1734803