AN EFFECTIVE SEQUENTIAL QUADRATIC PROGRAMMING ALGORITHM FOR NONLINEAR OPTIMIZATION PROBLEMS

摘要

In this paper, a new globally convergent algorithm for nonlinear optimization problems with equality and inequality constraints is presented. The new algorithm is of SQP type which determines a search direction by solving a quadratic programming subproblem per iteration. Some revisions on the quadratic programming subproblem have been made in such a way that the associated constraint region is nonempty for each point x generated by the algorithm, i.e. , the subproblems always have optimal solutions. The new algorithm has two important properties. The computation of revision parameter for guaranteeing the consistency of quadratic subproblem and the computation of the second order correction step for superlinear convergence use the same inverse of a matrix per iteration, so the computation amount of the new algorithm will not be increased much more than other SQP type algorithms; Another is that the new algorithm can give automatically a feasible point as a starting point for the quadratic subproblems per iteration, this will obivously simplify the computation procedure of the subproblems. Some numerical results are reported.