An improved sequential quadratic programming algorithm for solving general nonlinear programming problems

Abstract

In this paper, a class of general nonlinear programming problems with inequality and equality constraints is discussed.Firstly, the original problem is transformed into an associated simpler equivalent problem with only inequality constraints. Then, inspired by the ideals of sequential quadratic programming (SQP) method and the method of system of linear equations (SLE), a new type of SQP algorithm for solving the original problem is proposed. At each iteration, the search direction is generated by the combination of two directions, which are obtained by solving an always feasible quadratic programming (QP) subproblem and a SLE, respectively. Moreover, in order to overcome the Maratos effect, the higher-order correction direction is obtained by solving another SLE. The two SLEs have the same coefficient matrices, and we only need to solve the one of them after a finite number of iterations. By a new line search technique, the proposed algorithm possesses global and superlinear convergence under some suitable assumptions without the strict complementarity. Finally, some comparative numerical results are reported to show that the proposed algorithm is effective and promising.Keywords: general nonlinear programming, sequential quadratic programming, method of quasi-strongly sub-feasible directions, global convergence, superlinear convergence 2000 MSC: 49M37, 90C26, 90C30, 90C55

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