New Predictor–Corrector Algorithm for Symmetric Cone Horizontal Linear Complementarity Problems

• Published in: Journal of optimization theory and applications Vol. 202; no. 1; pp. 50 - 75
• Main Authors: Darvay, Zsolt, Rigó, Petra Renáta
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.07.2024; Springer Nature B.V
• Subjects: Algorithms; Applications of Mathematics; Calculus of Variations and Optimal Control; Optimization; Cartesian coordinates; Engineering; Linear programming; Mathematics; Mathematics and Statistics; Operations Research/Decision Theory; Optimization; Predictor-corrector methods; Theory of Computation; Predictor–corrector interior-point algorithm; Horizontal linear complementarity problem; Cartesian product of symmetric cones; Euclidean Jordan algebra; Algebraically equivalent transformation technique
• ISSN: 0022-3239; 1573-2878; 1573-2878
• DOI: 10.1007/s10957-022-02078-z

We propose a new predictor–corrector interior-point algorithm for solving Cartesian symmetric cone horizontal linear complementarity problems, which is not based on a usual barrier function. We generalize the predictor–corrector algorithm introduced in Darvay et al. (SIAM J Optim 30:2628–2658, 2020) to horizontal linear complementarity problems on a Cartesian product of symmetric cones. We apply the algebraically equivalent transformation technique proposed by Darvay (Adv Model Optim 5:51–92, 2003), and we use the difference of the identity and the square root function to determine the new search directions. In each iteration, the proposed algorithm performs one predictor and one corrector step. We prove that the predictor–corrector interior-point algorithm has the same complexity bound as the best known interior-point methods for solving these types of problems. Furthermore, we provide a condition related to the proximity and update parameters for which the introduced predictor-corrector algorithm is well defined.