A Modified Sqp Algorithm For Nonlinearly Inequality Constrained Optimization

The sequential quadratic programming (SQP) algorithm is an important class of iterative methods for solving constrained optimization problems. They are particularly welcome methods for the solution of the small and medium size problems. In this thesis, we make some modification to some existing sequential quadratic programming (SQP) algorithm for solving inequality constrained problems. We also do some numerical experiments and compare the performance of the proposed method with some existing SQP methods. The results show that the proposed method performs better than the compared method.The basic idea of the traditional SQP algorithm is as follows. Starting from some initial guess to the solution x0, the method generate a sequence of iterate {xk}. At each iteration, the method solves one or several quadratic programming sub-problems to get a better approximate solution. In general, the iterates generated by an SQP method are not feasible. So to get the next iterate, it generally needs some penalty function as the merit function. The penalty factor in general should be very large, which may cause dificulty in the computation. In addition, the solution of the quadratic subproblems are also time consuming. To save the computation cost, in this thesis, we meke some modification some existing SQP method and proposed a modifiec SQP method (called MSQP method). The MSQP method is an improvement to the existing SQP method and enjoys some nice properties. At each iteration, we only need to solve one quadratic subproblem. In addition, after finitely many iterations, the method generates a sequence of iterates that are feasible for the inequality constrained problem. Under appropriate conditions, we prove that the global and superlinear convergence of the MSQP method. It is worth noting that the superlinear convergence of MSQP algorithms is achieved without the requirement of the strict complementarity condition at the solution.