An algorithm of feasible directions to mixed nonlinear complementarity problems and applications

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Ramírez Gutiérrez, Ángel Enrique
Ramírez Gutiérrez, Ángel Enrique
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Universidad Nacional de Ingeniería
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This work investigates the Feasible Direction Algorithm using interior points applied to the Mixed Nonlinear Complementarity Problem and some applications. This algorithm is based in Feasible Directions Algorithm for Nonlinear Complementarity Problem, which is described briefly. The proposed algorithm is important because many mathematical models can be written as mixed nonlinear complementarity problem. The principal idea of this algorithm is to generate, at each iteration, a sequence of feasible directions with respect to the region, defined by the inequality conditions, which are also monotonic descent directions for one potential function. Then, an approximate line search along this direction is performed in order to define the next iteration. Global and asymptotic convergence properties for the algorithm are proved. In order to validade the robustness the algorithm is tested on several benchmark problems, that were found in the literature, considering the same para- meters. In this work one dimensional models describing Oxygen Diffusion inside one cell and In Situ Combustion are also presented together with bidimensional model of the Elastic-Plastic Torsion Problem. These models are re-written as nonlinear com¬plementarity problem and mixed nonlinear complementarity problem. These new formulations are discretized by Finite Diference Scheme or Finite Element Method and, for its discrete forms, the algorithm will be applied. The numerical results are compared with direct numerical simulation using Newton’s method (in the case of Oxygen Diffusion and In Situ Combustion) or exact solution (in the case of Elastic- Plastic Torsion Problem). It is shown that the obtained results are in good agreement with the asymptotic analysis. For the In situ combustion model the corresponding Riemann’s problem is studied in order to validate numerical solutions.
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Complementariedad no lineal mixta, Algoritmo de direcciones factibles