A Partially Feasible Distributed Sequential Quadratic Programming Algorithm For Two-block Smooth Optimization With General Linear Constraints

This dissertation discusses the two-block smooth optimization problem with general linear constraints,and aims to establish a novel partially feasible distributed sequential quadratic programming(PFD-SQP)algorithm.The constructed optimization problem with separable structure is used in practical engineering.It has a wide range of applications,such as power system economic dispatch,data mining,signal processing,etc.Therefore,it is of great scientific value and practical significance to study an effective solution method for its special structure.Alternating direction multiplier method(ADMM)and sequential quadratic programming(SQP)algorithm are very effective methods for solving constrained optimization problems.ADMM can decompose a large-scale problem into several smaller-scale problems to be solved alternately,thus reducing the difficulty of solving and the computational cost.The SQP algorithm has the advantages of good convergence properties and fast convergence speed,and is especially suitable for solving small and medium-scale smooth optimization problems with constraints.The PFD-SQP algorithm takes the SQP algorithm as the main line.When solving the quadratic programming(QP)sub-problem,it draws on the idea of distributed ADMM and decomposes it into two completely independent and small-scale QPs for parallel solving.An appropriate and adjustable perturbation shrinkage term is innovatively introduced to the inequality constraint in solving the small-scale QP,so that the feasible step size can be increased and even reach 1.Then,using the Lagrangian function as the benefit function,the Armijo line search is used to generate new iteration points.Firstly,this dissertation first gives the construction idea and main steps of the PFD-SQP algorithm,and analyzes and demonstrates its convergence under appropriate assumptions.Secondly,the strong convergence and iterative complexity of the PFD-SQP algorithm are analyzed.Finally,the numerical validity of the PFD-SQP algorithm is verified by a class of mathematical examples and the economic dispatch model of the power system.