From: Kernel function based interior-point methods for horizontal linear complementarity problems
Step 0 | Define the kernel function ψ(t) and input initial values: τ ≥ 1, ϵ>0, 0<θ<1, , and such that . |
Step 1 | Solve the equation to find ρ(z), the inverse function of , 0<t ≤ 1. If the equation is hard to solve, compute a lower bound for ρ(z). |
Step 2 | Solve the equation ψ(t)=u to find ϱ(u), the inverse function of ψ(t), t ≥ 1. If the equation is hard to solve, compute an upper bound for ϱ(u). |
Step 3 | Compute a lower bound for δ with respect to Ψ. |
Step 4 | Compute the upper bound for Ψ(v). |
Step 5 | Using Step 3, Step 4 and the default step size in (22), find λ>0 and γ, 0<γ ≤ 1, as small as possible such that . |
Step 6 | Derive an upper bound for the total number of iterations from . |
Step 7 | Let and θ = Θ(1) to compute an iteration bound for large-update method, and let and to get an iteration bound for small-update method. |