A Novel Full NT-Step Infeasible Interior-Point Algorithm for Semi-Definite Linear Complementarity Problems: Convergence and Numerical Performance

This paper presents an improved infeasible interior-point algorithm tailored for semi-definite linear complementarity problems (SDLCPs). The proposed approach leverages full Nesterov–Todd search directions while eliminating centering steps, significantly simplifying the algorithmic structure and reducing computational overhead. A rigorous theoretical analysis confirms that the method is well defined, globally convergent, and achieves an iteration complexity that matches the best-known bounds for infeasible interior-point methods in this domain. Complementing the theoretical results, extensive numerical experiments highlight the algorithm’s superior practical performance, consistently achieving faster convergence with fewer iterations compared to existing methods. These findings demonstrate the algorithm’s potential as an efficient and robust solution technique for SDLCPs, with promising applicability to large-scale and complex problem instances.