Primal-dual Algorithms Based On BB Stepsize For Structural Optimization Problems

In this thesis,we study the numerical methods for quadratic convex optimization problems with linear equality constraints.The usual ways to solve this kind of problems are augmented Lagrangian method(ALM)and alternating direction method of multipliers(ADMM).However,the rate of convergence would be affected by the selection of penalty parameters.We borrow the ideal of BB algorithm for unconstrained convex optimization problems to improve the original ALM and ADMM algorithms.Firstly,we propose the improved ALM-BB algorithm and prove its convergence.Secondly,we analyze the insufficiency of the ADMM-BB algorithm and give two types of correction algorithms.Finally,some numerical examples of optimal control problem are given to show the effectiveness of the ALM-BB and modified ADMM-BB algorithms.