Research On Splitting Sequential Quadratic Programming Algorithms For Nonseparable Nonconvex Optimization Problems With Nonlinear Constraints

This dissertation discusses the nonseparable nonconvex optimization problem with nonlinear constraints,The optimization problem with separable structure is widely used in practical engineering.Therefore,it is of practical significance and great scientific value to study an effective solving method for this special structure.The splitting sequential quadratic programming(SQP)algorithm takes use of advantages of alternating direction method of multipliers(ADMM)and SQP algorithm,and develops efficient new algorithms for block large-scale optimization.Based on splitting SQP in this dissertation,proposing two new splitting SQP algorithms for the nonseparable optimization problems with nonlinear equality constraints and general nonlinear constraints.Firstly,for the nonseparable nonconvex optimization problem with nonlinear equality constraints,inspired by the idea of Jacobian splitting,the augmented Lagrangian quadratic programming(QP)in the classical SQP method is decomposed into two small-scale QPs.Moreover,by taking the augmented Lagrangian function(ALF)as the merit function,the next iteration point is generated by the Armijo line search.Under the mild conditions,it can ensure the global convergence of the proposed algorithm.In addition,some numerical results are reported,which preliminarily show that the proposed algorithm is promising.Secondly,for extending the applicability of the above algorithm,the discussed problem is further expanded to nonseparable optimization problem with general nonlinear constraints,similarly,to decompose into two completely independent and small-scale QPs.The ideas of the feasible norm-relaxed SQP method and approximate active set technique are adopted to solve the two small-scale of QPs,so that the descent direction has good feasibility.Then,by using the ALF as the merit function,the next iteration point is generated by the Armijo line search.Under the mild conditions,the convergence and iterative complexity of the algorithm are proved.