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

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