Study Of The Parallel Variable Distribution Algorithms Of Quadratic Programming

In this paper, modified SQP type parallel variable distribution (PVD) algorithms are proposed for the special constraints with block-separable structure, and the global convergence of these methods are established. The paper is organized as follows:In Chapter 1, we introduce the development and the current research situations of the parallel optimization algorithms as well as the main work of the thesis.In Chapter 2, we give the existed parallel variable distribution algorithms.In Chapter 3, we give a feasible parallel algorithm. It overcomes the disadvantages of the existing SQP type PVD algorithm in 2002. In our algorithm the search direction is a suitable combination of a descent direction, a feasible direction and a second-order revised direction. This new algorithm is very effective in preventing the occurrence of maratos effect and can circumvent the difficulties associated with the possible inconsistency of quadratic programming subproblems or their solutions are unbounded.In Chapter 4, we introduce an infeasible parallel algorithm. Here we introduce a linear programming, so at each iteration we need to solve a linear programming and a quadratic programming rather than the original quadratic programming subproblem in 2002, in this case the difficulties associated with the possible inconsistency of subproblem in the original method could be avoid. Moreover, we introduce a non-monotone technique instead of the penalty function to carry out the line search procedure with more flexibly.In Chapter 5, a PVD algorithm for constrained optimization with non-monotone technique is proposed, which solves a modified quadratic subproblem at each iteration point instead of the quadratic programming subproblems in the original PVD algorithm. The algorithm can circumvent the difficulties associated with the possible inconsistency of subproblems or their solutions are unbounded. Moreover, we introduce a non-monotone technique of object function instead of the penalty function to carry out the line search procedure, and overcome the drawback that the penalty parameter estimates could be problematic to obtain.In Chapter 6, we give conclusions and expectations of the parallel algorithm.