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|Title:||A quadratically convergent polynomial long-step algorithm for a class of nonlinear monotone complementarity problems|
|Authors:||Sun, J. |
|Keywords:||Complexity of algorithms|
Interior point methods
Monotone complementarity problems
Rate of convergence
|Source:||Sun, J.,Zhao, G. (2000). A quadratically convergent polynomial long-step algorithm for a class of nonlinear monotone complementarity problems. Optimization 48 (4) : 453-475. ScholarBank@NUS Repository.|
|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. © 2000 OPA (Overseas Publishers Association) N.V. Published by license under the Gordon and Breach Science Publishers imprint.|
|Appears in Collections:||Staff Publications|
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