Research The Algorithms Solving Convex Quadratic Programming With Linear Constraints

The quadratic programming problem is an important research field of nonlinear optimization,and it has many applications in real life.The main research object of the thesis is the algorithm of solving convex quadratic programming problem with linear constraints.The thesis starts with the equality-constrained convex quadratic programming problem,explores its solution,and further introduces three methods to solve the non-equality-constrained convex quadratic programming problem,including the active set method,interior point method and gradient projection method.What's more,the gradient projection method based on the properties of CQP image is proposed by the analysis and summary of various algorithm ideas.Through numerical experiments,the thesis verifies the feasibility of the active set method,the primal-dual path following method and the gradient projection method,the adaptability to problems of different dimensions and the convergence in the feasible region.Moreover,it also verifies the feasibility of the gradient projection method based on the properties of CQP image,and preliminarily verifies that the improved method can indeed reduce the number of iterations and improve the computational efficiency.