Implementation of an Interior-point Algorithm for Linear Complementarity Problem Working in a Wide Neighborhood


In this article, we study the interior-point algorithm for solving linear complementarity problems, published by Xiaouje Ma, Hongwei Liu, Jianke Zhang and Weijie Cong from the implementation point of view. The algorithm was implemented in C++ programming language, thus supporting the effectiveness of the method. Despite the fact that the theoretical results refer only to the monotone linear complementarity problem, practical testing showed that the algorithm also works well in more general cases.

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  • [1] Roos C., Terlaky T., Vial. J.-Ph.: Theory and Algorithms for Linear Optimization. Springer, NY, USA, 2005.

  • [2] Wright. S. J.: Primal-Dual Interior-Point Methods. SIAM, Philadelphia, USA, 1997.

  • [3] Ye. Y.: Interior Point Algorithms, Theory and Analysis. John Wiley & Sons, Chichester, UK, 1997/3. (1997)

  • [4] Kojima M., Megiddo N., Noma T., Yoshise A.: A Unifed Approach to Interior Point Algorithms for Linear Complementarity Problems. Lecture Notes in Computer Science 538, Springer Verlag, Berlin, Germany, 1991.

  • [5] Ai. W.: Neighborhood-following algorithm for linear programming. Sci. China serie A, 47. (2004) 812 – 820.

  • [6] Ai W., Zhang S.: An O(√nL) iteration primal-dual path-following method, based on wide neighborhoods and large updates, for monotone LCP. SIAM Journal on Optimization 16/2. (2005) 400–417.

  • [7] Ma X., Liu H., Zhang J., Cong W.: On superlinear and O(√nL) convergence of a path-following algorithm for monotone linear complementarity problems in a wide neighborhood. Numerical Functional Analysis and Optimization, 38/5. (2017) 627–640.

  • [8] Darvay Zs., Takó I.: Computational comparison of primal-dual algorithms based on a new software. unpublished manuscript. (2012)

  • [9] Hock W., Shittkowski K.: Test Examples for Nonlinear Programming Codes. Lecture Notes in Economics and Mathematical Systems 187. Springer, Berlin (1981)

  • [10] Harker P. T., Pang J. S.: A damped Newton method for linear complementarity problem. In: Simulation an Optimization of Large Systems, Lectures on Applied Mathematics, AMS, Providence, RI, 26. (1990) 265–284.

  • [11] Morapitiye S.: Sufficient Matrices. (accessed on 9 February 2019).

  • [12] Darvay Zs., Illés T., Povh J., Rigó P. R.: Predictor-corrector interior-point algorithm for sufficient linear complementarity problems based on a new search direction, manuscript. (2019)


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