Research On Monotone Symmetric Distributed SQP Algorithm Based On Quadratic Approximation For Nonseparable Smooth Optimization

With the advent of the “big data” era,the scale of data shows exponential growth,and the large-scale optimization driven by this has become a scientific problem to be solved urgently in most fields.On the strength of the idea of complementary advantages and combining the advantages of the alternating direction method of multipliers(ADMM)and sequential quadratic programming(SQP),Prof.Jian Jinbao et al.proposed a ADMM-SQP algorithm for linear constrained two-block optimization in 2018.This algorithm fully absorbed the advantages of ADMM decomposition dimension reduction and SQP algorithm efficient solution and applied the advantages of splitting to the solving of large-scale quadratic programming(QP)subproblem,which reduced the scale of the QP subproblem,thus bringing down the difficulty and cost of solving the problem to strive to improve or make the algorithm have better convergence and numerical effect.The research on the combination of split algorithm and SQP algorithm has important theoretical and practical significance for constructing a new split SQP algorithm.The monotone distributed SQP algorithm proposed in this paper is a new efficient optimization algorithm for large-scale nonconvex nonseparable smooth optimization.The algorithm takes the sequential quadratic constrained quadratic programming as the main line,introduces the splitting idea into the quadratic programming subproblem,and transforms the subproblem into standard QP subproblem by reasonable approximation.First,the small scale QP subproblem of the first set of variables x is solved to generate its improvement direction,and then the Armijo line search is performed based on the augmented Lagrangian merit function to generate the “middle” primal-dual iteration points.Secondly,based on these points,we design and solve the QP subproblem about the second set of variables y and generate its search direction,and then produce new iteration points by Armijo line search about y.The convergence of the algorithm is analyzed systematically.Finally,numerical experiments are carried out on two kinds of problems,one is a type of mathematical example,and the other is the economic dispatch model of power system.