Line Search Filter Sequential Quadratic Programming Method For Solving Nonlinear Inequality Constrained Optimization Problem

Optimization method (also called operations research method) isnearly a few years to form, which is mainly the use of mathematicalmethods for the study of various methods for optimizing the system andsolutions, to provide the scientific basis for decision-making.Optimization method for main research object is the variousorganization system management problems and its production andmanagement activities. Optimization method aimed to researchsystem, to obtain a reasonable use of human, material and financialresources to the best solution, play and improve the systemperformance and efficiency, ultimately achieve system optimization.Practice shows that, with the increasing progress of science andtechnology and production development, the optimization methodhas become the modern management science important theoreticalbasis and indispensable method, is widely applied to all areas of society,plays a more and more important role.Filter methods are extensively studied for solving nonlinearprogramming problems (NLP). Fletcher and Leyffer first introduced filtermethods for nonlinear constrained optimization, instead of thetraditional merit function method, as a tool to ensure the globalconvergence of algorithm for solving nonlinear programming. The mainidea of this method is that trail points are accepted if they improve theobjective function or improve the constraint violation instead of acombination of those two measures defined by a merit function. In thispaper, we propose the sequence quadratic programming method witha line search filter technique for nonlinear inequality constrainedproblems.The sequential quadratic programming (SQP) approach can beused both in line search and trust-region frameworks, and it is appropriate for small or large problems. SQP methods show theirstrength when solving problems with significant nonlinaerities. In thispaper, the search direction is generated by solving quadraticsubproblems and first-order necessary conditions. We use the active setto treating the inequality constraints. We would employ second ordercorrection to overcome the Maratos effect.The thesis consists of three parts. In Chapter1, we summarize thebasic concepts of optimization technique and the basic structure of theoptimization method. In Chapter2, we proposed a line search filter-SQPmethod for nonlinear inequality constrained optimization and provedthe global and local convergence. Finally, in Chapter3, we concludethe main results of this thesis and propose some further researchdirections about our work.