Unified approach of primal-dual interior-point algorithms for a new class of AET functions

Tibor Illés, Petra Renáta Rigó and Roland Török

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

Abstract: We propose new short-step interior-point algorithms (IPAs) for solving P_* (κ)-linear complementarity problems (LCPs). In order to define the search directions we use the algebraic equivalent transformation technique (AET) of the system which characterizes the central path. A novelty of the paper is that we introduce a new class of AET functions. We present the complexity analysis of the IPAs that use this general class of functions in the AET technique. Furthermore, we also deal with a special case, namely φ(t)=t^2-t+√t. This function differs from the ones used in the literature in the sense that it has inflection point. It does not belong to the class of concave functions determined by Haddou et al. Furthermore, the kernel function corresponding to this AET function is neither eligible nor self-regular kernel function. We prove that the IPAs using any member φ of this new class of AET functions have polynomial iteration complexity in the size of the problem, bit length of the integral data and in the parameter κ. Beside this, we also provide numerical results that show the efficiency of the introduced methods.

Keywords: Interior-point algorithm; P∗ (κ)-linear complementarity problem; algebraic equivalent transformation technique; new class of AET functions (search for similar items in EconPapers)
JEL-codes: C61 (search for similar items in EconPapers)
Date: 2022-02-18
New Economics Papers: this item is included in nep-ore
References: Add references at CitEc
Citations:

Downloads: (external link)
https://unipub.lib.uni-corvinus.hu/7197/ original version (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:cvh:coecwp:2022/02

Access Statistics for this paper

More papers in Corvinus Economics Working Papers (CEWP) from Corvinus University of Budapest 1093 Budapest, Fõvám tér 8.. Contact information at EDIRC.
Bibliographic data for series maintained by Adam Hoffmann ().