Filter And Improved Filter Methods For Nonlinear Constrained Programming

Optimization is an emerging discipline which has a strong content. It is an importantbranch of applied mathematics. Optimization is to obtain the best solution among themany given methods in practical problems. With the development of science, nonlinearconstrained programming plays more and more important role in the real life. So thestudy of method is essential.Sequential quadratic programming method is one of the most efective methods. ButThe sequential quadratic programming may not convergent if the initial point is far awayfrom the solution. To solve the problem, many authors always use the penalty function.But, for penalty function, its penalty parameter is difcult to obtain. To overcome thisproblem, filter method is proposed by Fletcher and Leyfer in2002. Because of thegood numerial results, filter method is studied by more and more authors. Since thefilter acceptance criterion requires that the trial point compares with all the points inthe filter, it implies that all the information about the points in the filter are needed.Another penalty-free-type method is proposed.The major new results of this thesis contain the following two respects:(i) Thereare two aspects for improving the filter method. Firstly, a tri-dimensional filter methodis proposed which relaxes the acceptable criterion. Secondly, an active set sequentialquadratic programming filter method is presented by reducing size of quardratic pro-gramming subproblem.(ii) The kind of penalty-free-type method is presented. Thereare two methods. Firstly, the modified quadratic subproblem is feasible whether trialpoint is a feasible point or not. A penalty-free-type method is proposed. Secondly,by non-monotone technique, an improved sequential quadratic programming method isproposed, which relaxes the acceptance condition.