Kernel function based interior-point methods for horizontal linear complementarity problems

Journal of Inequalities and Applications

Table 2 The first two derivatives of the kernel functions

j	$ψ_{j}^{'} (t)$	$ψ_{j}^{''} (t)$
1	$e t - e^{p (g_{1} (t) - e)} g_{1} (t) t^{- r - 1}$	$e + e^{p (g_{1} (t) - e)} g_{1} (t) t^{- 2 r - 2} (p r g_{1} (t) + r + (r + 1) t^{r})$
2	$t - e^{p (g_{2} (t) - 1)} g_{2} (t) t^{- r - 1}$	$1 + e^{p (g_{2} (t) - 1)} g_{2} (t) t^{- 2 r - 2} (p r g_{2} (t) + r + (r + 1) t^{r})$