Modified QP-free Methods For Constrained Optimization Problem Without Penalty Function

Nonlinear constrained optimization problems,with nonlinear objective function or nonlinear constraint functions,arise in many fields,such as operation management,engineer design,scientific research,military command and so on.Therefore,it is important to research the methods for solving nonlinear constrained programming.With the rapid development of computer technology,various methods have been proposed.As we all know,sequential quadratic programming method(SQP)is one of the most effective methods for nonlinear constrained optimization problems.However,there are some drawbacks in SQP method,for example,the incompatibility of the quadratic subproblem,and large computational scale caused by the solving the quadratic subproblems in each iteration.To avoid the drawbacks,various QP-free methods are proposed gradually.In this thesis,several modified nonmonotonic QP-free methods without penalty function are presented for general nonlinear constrained optimization problems based on different working sets.Firstly,based on the search direction and the corresponding lagrangian multiplier or the constrained functions,we modify the right hand side of the equation with convex combination technique to obtain the search direction.Then together with the nonmonotone filter technique,we present a modified nonmonotonic filter QP-free method.Secondly,a new QP-free method without a penalty function or a filter is proposed in order to deal with the large storage of filter pairs.And a new balance mechanism is constructed to balance the objective function and the constraint violation function.Finally,a new and more relaxed nonmonotonic idea is constructed.The subproblem of QP is obtained by perturbing the first order approximation of constraint,and then the search direction is bent by Lagrangian information.In the end,the global convergent properties are given,and numerical results show that the algorithms are effective and easy to implement.