Full Nesterov-Todd step feasible interior-point algorithm for symmetric cone horizontal linear complementarity problem based on a positive-asymptotic barrier function. (2nd January 2022)

• Record Type: Journal Article
• Authors: Asadi, S.; Mahdavi-Amiri, N.; Darvay, Zs.; Rigó, P. R.
• Is Part Of: Optimization methods and software. Volume 37:Number 1(2022)
• Page Start: 192
• Page End: 213
• Publication Date: 2022-01-02
• Subjects: Cartesian symmetric cone horizontal linear complementarity problem -- Euclidean Jordan algebra -- positive-asymptotic barrier function -- Algebraic transformation of the central path -- Nesterov-Todd directions; 90C51 -- 90C33; Mathematical optimization -- Periodicals; Algorithms -- Periodicals; 519.7
• DOI: 10.1080/10556788.2020.1734803
• Languages: English
• ISSNs: 1055-6788

Abstract

Abstract : We present a feasible full step interior-point algorithm to solve the P ∗ ( κ ) 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.