N∞− neighbourhood of the central path
References
- W.B. Ai and S.Z. Zhang, An O(nL) iteration primal-dual path following method, based on wide neighborhoods and large updates, for monotone linear complementarity problems, SIAM J. Optim. 16(2) (2005), pp. 400–417. doi: 10.1137/040604492
- S. Asadi and H. Mansouri, A full-Newton step infeasible-interior-point algorithm for P∗(κ)-horizontal linear complementarity problem, Yugosl. J. Oper. Res. 25(1) (2015), pp. 57–72. doi: 10.2298/YJOR130515034A
- N.K. Karmarkar, A new polynomial-time algorithm for linear programming, Combinatorica 4 (1984), pp. 373–395. doi: 10.1007/BF02579150
- B. Kheirfam, A new complexity analysis for full-Newton step infeasible interior-point algorithm for horizontal linear complementarity problems, J. Optim. Theory Appl. 161(3) (2014), pp. 853–869. doi: 10.1007/s10957-013-0457-7
- B. Kheirfam, A full step infeasible interior-point method for Cartesian P∗(κ)-SCLCP, Optim. Lett. 10(3) (2016), pp. 591–603. doi: 10.1007/s11590-015-0884-5
- B. Kheirfam, An improved full-Newton step O(n) infeasible interior-point method for horizontal linear complementarity problem, Numer. Algorithms 71(3) (2016), pp. 491–503. doi: 10.1007/s11075-015-0005-7
- M. Kojima, N. Megiddo, T. Noma, and A. Yoshise, A Unified Approach to Interior Point Algorithms for Linear Complementarity Problems, Lecture Notes in Computer Science 538, Springer-Verlag, Berlin, 1991.
- F.A. Potra, Interior point methods for sufficient horizontal LCP in a wide neighborhood of the central path with best known iteration complexity, SIAM J. Optim. 24(1) (2014), pp. 1–28. doi: 10.1137/120884341
- F.A. Potra and J. Stoer, On a class of superlinearly convergent polynomial time interior point methods for sufficient LCP, SIAM J. Optim. 20(3) (2009), pp. 1333–1363. doi: 10.1137/080716979
- B.K. Rangarajan, Polynomial convergence of infeasible interior-point methods over symmetric cones, SIAM J. Optim. 16(4) (2006), pp. 1211–1229. doi: 10.1137/040606557
- C. Roos, A full-Newton step O(n) infeasible interior-point algorithm for linear optimization, SIAM J. Optim. 16(4) (2006), pp. 1110–1136. doi: 10.1137/050623917
- G.Q. Wang and Y.Q. Bai, Polynomial interior-point algorithms for P∗(κ) horizontal linear complementarity problem, J. Comput. Appl. Math. 233(2) (2009), pp. 248–263. doi: 10.1016/j.cam.2009.07.014
- Y. Yang, A polynomial arc-search interior-point algorithm for linear programming, J. Optim. Theory Appl. 158(3) (2013), pp. 859–873. doi: 10.1007/s10957-013-0281-0
- X. Yang, Y. Zhang, and H. Liu, A wide neighborhood infeasible-interior-point method with arc-search for linear programming, J. Appl. Math. Comput. (2015). doi: 10.1007/s12190-015-0900-z.
- Y. Zhang, On the convergence of a class of infeasible interior-point algorithms for the horizontal linear complementarity problem, SIAM J. Optim. 4(1) (1994), pp. 208–227. doi: 10.1137/0804012