论文信息 - A combined homotopy interior point method for the linear complementarity problem

A combined homotopy interior point method for the linear complementarity problem

A combined homotopy interior point method for the linear complementarity problem (LCP) is proposed in this paper. We construct a homotopy path for the linear complementarity problem and prove that the homotopy path determines a smooth interior path from an arbitrary given interior point to the solution of LCP. Furthermore, we modify a predictor corrector algorithm with the technique of the cone neighborhood to trace the homotopy path. Finally, a numerical example is provided to show the effectiveness and feasibility of this method.

Xianjia Wang | Qian Yu | Chongchao Huang

[1] Shao-Liang Zhang,et al. The aggregate constraint homotopy method for nonconvex nonlinear programming , 2001 .

[2] Zheng-Hua Lin,et al. A combined homotopy interior point method for convex nonlinear programming , 1997 .

[3] Shinji Mizuno,et al. A primal—dual infeasible-interior-point algorithm for linear programming , 1993, Math. Program..

[4] Yin Zhang,et al. On the Convergence of a Class of Infeasible Interior-Point Methods for the Horizontal Linear Complementarity Problem , 1994, SIAM J. Optim..

[5] Yinyu Ye,et al. On quadratic and $$O\left( {\sqrt {nL} } \right)$$ convergence of a predictor—corrector algorithm for LCP , 1993, Math. Program..

[6] Narendra Karmarkar,et al. A new polynomial-time algorithm for linear programming , 1984, Comb..

[7] Yu Bo,et al. A combined homotopy interior point method for general nonlinear programming problems , 1996 .

[8] Stephen J. Wright. An infeasible-interior-point algorithm for linear complementarity problems , 1994, Math. Program..