Two Classes Of Filter Method For Constrained Optimization Problem And Its Application In Lot-Sizing Model

In this paper, we mainly study two filter methods of constrained optimization problem for arbitrary initial point and use one of these methods in lot-sizing model.A new generalized gradient projection filter method for arbitrary initial point is proposed at first. It can decrease the scale of computation and avoid the defect of penalty function. Another merit of the algorithm is that it avoids the filter converging to a feasible but non-optimal point or occurring cycling. Moreover, it has no demand on the initial point and under some mild assumptions it has global convergence.Combined with branch and bound method the above filter algorithm can solve mixed integer programming. We consider a single-buyer single-supplier system. The market demand for ordering business price is sensitive. Both the buyer and the supplier operate with unit product costs, inventory holding costs, and order placement costs. In addition, the buyer is responsible for the freight cost. Thus we can get an optimal batch and pricing of mixed integer programming model using the above algorithm. The algorithm is effective based on the calculation results.Combined with norm-relaxed method the filter algorithm could avoid incompatible of the QP-subproblem. To overcome the Maratos effect, another correction direction is given. Based on the global convergence of norm-relaxed filter method and some reasonable assumption, we prove the superlinearly convergence of the algorithm.