COMPLEXITY ANALYSIS OF LARGE-UPDATE INTERIOR-POINT METHODS FOR 𝓟∗(𝜿)-HLCP BASED ON A NEW PARAMETRIC KERNEL FUNCTION

This work proposes a primal-dual interior point technique for 𝒫∗(𝜅)-Horizontal Linear Complementarity Problem (𝒫∗(𝜅)-HLCP), based on a novel parameterized kernel function. Our new eligible parametric kernel function’s feature produces the following iteration bound 𝑂(((𝑝+1)(𝑛𝑝)𝑝+22(𝑝+1)⁄𝑙𝑜𝑔(𝑛𝜀))) for the large-update method. Finally, we present numerical results demonstrating the algorithm’s pratical performance among various parameters.