Solve The Quasi-separable MDO Problems By The MPCPM Method

Nonlinear programming problems is abound in many important fields, suchas,engineering, national defense, finance etc. There are many ways to solve theproblem of nonlinear planning in the small-scale problems. In order to solve theproblem, the scale of the method is not much and the decomposition method is tosolve the problem of a more efficient methods. The aim of decomposition inoptimization is to substitute large-scale optimization problems that present astructure of interrelated subsystems by solutions of subproblems.Multidisciplinary optimization design was the foreland of the modem designdevelopment methodology and a new multidisciplinary intercross fietd developed inrecent decade.It emphasized by using the newest accomplishment of computer scienc-e and technology,with the effective methodology of optimization designrealize thesystem idea incomplex engineering design．Several decomposition methods have been proposed for the distributed optimaldesign of quasi-separable problems encountered in Multidisciplinary DesignOptimization (MDO). Some of these methods are known to have numericalconvergence difficulties that can be explained theoretically. We propose a newdecomposition algorithm for quasi-separable MDO problems.In particular, wepropose a decomposed problem formulation based on the augmented Lagrangianpenalty function and the block coordinate descent algorithm.The proposed solutionalgorithm consists of inner and outer loops.In the outer loop, the augmentedLagrangian penalty parameters are updated. In the inner loop, our method alternatesbetween solving an optimization master problem and solving disciplinaryoptimization subproblems. The coordinating master problem can be solvedanalytically; the disciplinary subproblems can be solvedusing commonly availablegradient-based optimization algorithms. The augmented Lagrangian decompositionmethod is derived such that existing proofs can be used to show convergence of the decomposition algorithm to Karush-Kuhn-Tucker points of the original problemunder mild assumptions. We investigate the numerical performance of the proposedmethod on two example problems.