Comprehensive Analysis of Kernel-Based Interior-Point Methods for P_* (κ) - LCP

Zsolt Darvay, Marianna E. Nagy, Goran Lesaja, Petra Renáta Rigó and Anita Varga
Authors registered in the RePEc Author Service: Marianna Eisenberg-Nagy

Corvinus Economics Working Papers (CEWP) from Corvinus University of Budapest

Abstract: We present an interior-point algorithmic framework for P_* (κ)-Linear Complementarity Problems that is based on a barrier function which is defined by a new class of univariate kernel functions called Standard Kernel Functions (SKFs). A unified, comprehensive complexity analysis of the generic interior-point method is provided and a general procedure to determine the iteration bounds for long-step and short-step versions of the method for the entire class of SKFs is developed. We illustrate the general procedure by determining the iteration bounds for several parametric SKFs which include all SKFs that appeared in the literature as special cases. In all cases, we matched the best iteration bounds obtained in the literature for these special cases of SKFs.

Keywords: Linear complementarity problems; P∗(κ)-matrix; Interior-point methods; Kernel functions; Polynomial complexity (search for similar items in EconPapers)
JEL-codes: C61 (search for similar items in EconPapers)
Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:cvh:coecwp:2024/03

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