A quadratically convergent polynomial long-step algorithm for A class of nonlinear monotone complementarity problems^*

^*he research is partially supported by Grant RP930033 of National University of Singapore

Abstract

Several interior point algorithms have been proposed for solving nonlinear monotone complementarity problems. Some of them have polynomial worst-case complexity but have to confine to short steps, whereas some of the others can take long steps but no polynomial complexity is proven. This paper presents an algorithm which is both long-step and polynomial. In addition, the sequence generated by the algorithm, as well as the corresponding complementarity gap, converges quadratically. The proof of the polynomial complexity requires that the monotone mapping satisfies a scaled Lipschitz condition, while the quadratic rate of convergence is derived under the assumptions that the problem has a strictly complementary solution and that the Jacobian of the mapping satisfies certain regularity conditions

Keywords:

• Complexity Of Algorithms
• Interior Point Methods
• Monotone Complemen­ Tarity Problems
• Rate Of Convergence

^*he research is partially supported by Grant RP930033 of National University of Singapore

^*he research is partially supported by Grant RP930033 of National University of Singapore

Notes

^*he research is partially supported by Grant RP930033 of National University of Singapore