Interior-point algorithm for symmetric cone horizontal linear complementarity problems based on a new class of algebraically equivalent transformations

Abstract We generalize a primal-dual interior-point algorithm (IPA) proposed recently in (Illés T, Rigó PR, Török R Unified approach of algorithms for new class AET functions, 2022) to $$P_*(\kappa )$$ P ∗ ( κ ) -horizontal linear complementarity problems (LCPs) over Cartesian product symmetric cones. The is based on the algebraic equivalent transformation (AET) technique with functions. modification functions where only two conditions are used as opposed three 2022). Furthermore, feasible that uses full Nesterov-Todd steps, hence, no calculation step-size necessary. Nevertheless, we prove IPA has iteration bound matches best known IPAs solving these types problems.