In recent work (Pandit and Kulkarni [Discrete Applied Mathematics, 244 (2018), pp. 155–169]), the independence number of a graph was characterized as maximum \(\ell _1\) norm solutions Linear Complementarity Problem (LCP) defined suitably using parameters graph. Solutions this LCP have another relation, namely, that they corresponded to Nash equilibria public goods game. Thus \( \ell _1 \) has ...

in this paper, we present a new path-following interior-point algorithm for -horizontal linear complementarity problems (hlcps). the algorithm uses only full-newton steps which has the advantage that no line searchs are needed. moreover, we obtain the currently best known iteration bound for the algorithm with small-update method, namely, , which is as good as the linear analogue.

An infeasible interior-point algorithm for mixed symmetric cone linear complementarity problems is proposed. Using the machinery of Euclidean Jordan algebras and Nesterov-Todd search direction, the convergence analysis of the algorithm is shown and proved. Moreover, we obtain a polynomial time complexity bound which matches the currently best known iteration bound for infeasible interior-point ...