The Research On The Algorithms Of Some Large-scale Quadratic Programming

This thesis deals with the topic of algorithms of some large-scale quadratic programming problems. In the economic managemen, financial decision-making and engineering, many problems are summed up in solving the above large-scale problems are very difficult. People need an effective algorithm of solving large-scale quadratic programming problem. To this, many scholars do a lot of research. Due to the limitations of computer hardware storage space, directly solving this sort of large-scale problem is very difficultly. So, based on these study large-scale quadratic programming problem has the extremely vital significance.In the first chapter, briefly introduces the theoretical basis of quadratic programming problem. Introduce the quadratic programming model, quadratic programming of optimality conditions and quadratic programming of decomposition conditions. Then, illustrate the main job.In the second chapter, introduces some large-scale quadratic programming problem solving methods. For example, active set truncated-newton algorithm for large-scale bound constrained minimization; the matrix decomposition algorithm of quadratic programming; The new algorithm of large-scale strict quadratic programming problem; new algorithm of large-scale convex quadratic programming with simple bound constraints.In the third chpaper, a new algorithm for solving large scale convex quadratic programming is proposed. We decompose a large scale convex programming into a serial of small scale ones whose solutions approximate that of the large scale quadratic programming. It is proved that the algorithm proposed is of the convergence.In the fourth chapter, introduces the optimization of parallel computing and algorithm, and analyses it's in solving large-scale quadratic programming problem the feasibility and the numerical simulation.In the fifth chapter, combined with the third chapter and the fourth chapter content, we first set up parallel multi-splitting iterative algorithm for solving large scale quadratic programming. The algorithm has less computational complexity and quicker velocity and is especially suitable for large scale problem. It is proved that the algorithm proposed is of the global convergence under the certain conditions.