A New Ai–Zhang Type Interior Point Algorithm for Sufficient Linear Complementarity Problems
  • Metaadatok
Tartalom: https://unipub.lib.uni-corvinus.hu/11115/
Archívum: Corvinus Kutatások
Gyűjtemény: Status = Published
Subject = Mathematics, Econometrics
Subject = Decision making
Type = Article
Cím:
A New Ai–Zhang Type Interior Point Algorithm for Sufficient Linear Complementarity Problems
Létrehozó:
Eisenberg-Nagy, Marianna
Varga, Anita
Kiadó:
Springer
Dátum:
2024
Téma:
Decision making
Mathematics, Econometrics
Tartalmi leírás:
In this paper, we propose a new long-step interior point method for solving sufficient linear complementarity problems. The new algorithm combines two important approaches from the literature: the main ideas of the long-step interior point algorithm introduced by Ai and Zhang and the algebraic equivalent transformation technique proposed by Darvay. Similar to the method of Ai and Zhang, our algorithm also works in a wide neighborhood of the central path and has the best known iteration complexity of short-step variants. However, due to the properties of the applied transforming function in Darvay’s technique, the wide neighborhood definition in the analysis depends on the value of the handicap. We implemented not only the theoretical algorithm but a greedy variant of the new method (working in a neighborhood independent of the handicap) in MATLAB and tested its efficiency on both sufficient and non-sufficient problem instances. In addition to presenting our numerical results, we also make some interesting observations regarding the analysis of Ai–Zhang type methods.
Nyelv:
angol
angol
Típus:
Article
PeerReviewed
Formátum:
application/pdf
Azonosító:
Eisenberg-Nagy, Marianna and Varga, Anita (2024) A New Ai–Zhang Type Interior Point Algorithm for Sufficient Linear Complementarity Problems. Journal of Optimization Theory and Applications, 202 (1). pp. 76-107. DOI 10.1007/s10957-022-02121-z <https://doi.org/10.1007/s10957-022-02121-z>
Kapcsolat:
10.1007/s10957-022-02121-z