A Generalized Strongly Subfeasible Algorithm For Mathematicalprograms With Nonlinear Complementarity Constraints

Mathematical Programs with Equilibrium Constraints is a kind of specail opti-mzation problem, which besides equality constraints and inequality constraints it also contain complementarity constraints. Because of this kind of Problems are wide use in economy, engineering design,game theory and so on, so in recent year more and more people pay attention to it.In this thesis, we discuss mathematical programs with nonlinear complementarity constraints. Because of the bad property of the equilibrium constraints,it is very difficult to study and solve it by the well-developed theory and methods for a standard smoothing nonlinear problems(SSNP). The algorithm's ideal is benint from the ideal of generalize projection technique and strongly subfeasible direction algorithm. It can be approximately describe as follows: Firstly, by the introductin of a perturbed parameter //, replace the complementarity constraints with a generalized function ,then (MPEC) can be reformulated equivalently nonlinear constraints programs. Secondly.combine the ideal of strongly subfeasible direction algorithm and generalized projction tech-nique,we setup a generalized strongly subfeasible direction algorithm. The algorithm possess global convergence.Under proper condition,the algorithm possess strongly con-vergence.This thesis devide into seven parts.Section 1: Introduction. Describe Mathematical Programs with Complementarity Constraints. Introduce the developed algorithm for (MPEC) and the difficulties.Section 2: preliminary knowledge. Introduce the knowledge which will be used in this thesis.Section 3: Assumptions,Algorithm and it's property. Given our algorithm and analyse the main property of this algorithm.Section 4: Algorithm's global convergence. Analyse and prove algorithm's global convergence.Section 5: Algorithm's strongly convergence. Analyse and prove : under proper condition, the algorithm possess strongly convergence.Section 6: Numerical experiment . Some preliminary numerical results are given.Section 7: Conclusion. Draw a conclusion.