New Violation Constrained Functions In The Filter SQP Method

The constrained nonlinear optimization problem (NLP) is an important re-search topic in mathematical programming fields. Many practical problems canbe reduced to be the constrained nonlinear optimization problems. The sequentialquadratic programming (SQP) is one of the most usual and effective methods insolving the constrained nonlinear optimization problems.Fletcher and Leyffer proposed the filter SQP method in [10] in 1998, theSQP method combined with the filter has the better convergence and numericaleffect. The concept of filter is fairly simple, which is that trial points are acceptedby filter provided there is a sufficient decrease in the objective function or violationconstrained function, where the violation constrained function defined is in orderto let the point where the value of it equals zero meet the constrained conditions inusual. In order to meet the KKT conditions as well as the constrained conditions,so it satisfies the necessary optimality conditions for problem(NLP), we replacethe violation constrained function, in this paper, by some new functions which arethe violation constrained functions defined by NCP function withε, weak NCPfunction and smooth approximating function, which make well use of the solutionsof QP subproblems and the information of dual variants(the multiplier vectors) inorder to make algorithms have the better convergence. In this paper, we mainlydiscuss the above functions and apply the violation constrained functions to filterSQP methods the algorithms, furthermore, we prove that the new algorithms haveglobal convergence and superlinear convergence under the mild conditions. We alsouse double-curved function to define the violation equality constrained subfunctionand the violation inequality constrained subfunction, and we prove it has goodconvergence and numerical effect. Lastly, Some preliminary numerical resultsindicate that these new methods are quite promising.The thesis carries out the discussion in six chapters.In chapter one, we first introduce the basic optimization knowledge and defineNCP function,weak NCP function and filter.In chapter two, we propose several new violation constrained functions, makesome analyses, discussions, comparsions, and give some lemmas and theories.In chapter three, we introduce the algorithm's basic procedure of filterNCP(weak NCP)function SQP method.In chapter four, we prove the convergence of three new violation constrainedfunctions, and show they have the good convergence. In chapter five, we take ad-vantage of the double-curved function to define the violation constrained function,and prove its convergence.In chapter six, we discuss the the realization of algorithms,and give numericalresults.