Improvement Of Method For Solving Nonlinear Complementtarity Problem Via Merit Function

The nonlinear complementarity problem is an important type ofcomplementarity problem. It has been the hotspot in the research of mathematical.Nonlinear complementarity problem has many important applications in differentfields such as economics equilibrium models, operations research, control theory,transportation, etc. In recent years, many algorithms have been proposed. In thispaper, we propose non-monotone algorithm for solving nonlinear complementarityproblem. The main content of the thesis is presented as follows:First, based on the traditional algorithm for solving nonlinear complementarityproblem. Nonlinear complementarity problem was reformulated as a nonnegativeconstrained optimization problem, by combining with Gu non-monotone-step linesearch technique, we propose a new non-monotone-step descent algorithm forsolving nonlinear complementarity problem. Under some reasonable conditions, itis proved that the algorithm is globally convergent. Numerical experiments showthat the new algorithm is effective.Next, Nonlinear complementarity problem can be reformulated as anunconstrained optimization problem by using F-B merit function. Based on Gunon-monotone-step line search technique, by combining with PRP+type conjugategradient method, we propose a new non-monotone-step conjugate gradientalgorithm for solving nonlinear complementarity problem. Under some reasonableconditions, it is proved that the algorithm is globally convergent. Numericalexperiments show that the new algorithm is effective, suitable to solve large scalenonlinear complementarity problems.Lastly, Use of Matlab program for the new algorithm in numerical experiments,results indicate that the new algorithm of non-monotone than Armijo monotonicalgorithm has a clear advantage, in the number of iterations, the new algorithmusing fewer; in the optimal solution for accuracy, a new algorithm for high precision;at run time, the new algorithms used in less time, increase the practicality andfeasibility of algorithms, and numerical algorithm to achieve satisfactory results.