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We present a sequential quadratic programming method without using a penalty function or a filter for solving nonlinear equality constrained optimization. In each iteration, the linearized constraints of the quadratic programming are relaxed to satisfy two mild conditions; the step-size is selected such that either the value of the objective function or the measure of the constraint violations is sufficiently reduced. As a result, our method has two nice properties. First, we do not need to assume the boundedness of the iterative sequence. Second, we do not need any restoration phase which is necessary for filter methods. We prove that the algorithm will terminate at either an approximate Karush–Kuhn–Tucker point, an approximate Fritz–John point, or an approximate infeasible stationary point which is an approximate stationary point for minimizing the l2 norm of the constraint violations. By controlling the exactness of the linearized constraints and introducing a second-order correction technique, without...

Multistage stochastic programming problems arise in many practical situations, such as production and manpower planning, portfolio selections, and so on. In general, the deterministic equivalents of these problems can be very large and may not be solvable directly by general-purpose optimization approaches. Sequential quadratic programming (SQP) methods are very effective for solving medium-size nonlinear programming. By using the scenario analysis technique, a decomposition method based on SQP for solving a class of multistage stochastic nonlinear programs is proposed, which generates the search direction by solving parallelly a set of quadratic programming subproblems with much less size than the original problem at each iteration. Conjugate gradient methods can be introduced to derive the estimates of the dual multiplier associated with the nonanticipativity constraints. By selecting the step-size to reduce an exact penalty function sufficiently, the algorithm terminates finitely at an approximate optimal solution to the problem with any desirable accuracy. Some preliminary numerical results are reported.