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 seve...

Alguns problemas parabólicos podem ser reescritos na forma de problema de complementaridade e aparecem em muitas aplicações como em fluxos de líquidos no interior num domínio, difusão, fluxo de calor envolvendo mudança de fase e reações químicas. Estes tipos de problemas apresentam muitas dificuldades analíticas e numéricas, normalmente devido à evolução no tempo ou fronteira móvel. Como a solução analítica é muito difícil de obter, é importante o estudo de métodos numéricos que permitam a busca de uma solução aproximada da solução exata para tais tipos de problemas. Estuda-se leis de conservação e os tipos de soluções associadas ao Problema de Riemann, essencialmente leis de balanço que expressam o fato de que alguma substância é conservada. O estudo desta teoría é importante porque frequentemente as leis de conservação aparecem quando nos problema...

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 seve...