This paper discusses the two-block large-scale nonconvex optimization problem with general linear constraints.Based on the ideas of splitting and sequential quadratic optimization(SQO),a new feasible descent method fo...This paper discusses the two-block large-scale nonconvex optimization problem with general linear constraints.Based on the ideas of splitting and sequential quadratic optimization(SQO),a new feasible descent method for the discussed problem is proposed.First,we consider the problem of quadratic optimal(QO)approximation associated with the current feasible iteration point,and we split the QO into two small-scale QOs which can be solved in parallel.Second,a feasible descent direction for the problem is obtained and a new SQO-type method is proposed,namely,splitting feasible SQO(SF-SQO)method.Moreover,under suitable conditions,we analyse the global convergence,strong convergence and rate of superlinear convergence of the SF-SQO method.Finally,preliminary numerical experiments regarding the economic dispatch of a power system are carried out,and these show that the SF-SQO method is promising.展开更多
This work discusses a class of two-block nonconvex optimization problems with linear equality,inequality and box constraints.Based on the ideas of alternating direction method with multipliers(ADMM),sequential quadrat...This work discusses a class of two-block nonconvex optimization problems with linear equality,inequality and box constraints.Based on the ideas of alternating direction method with multipliers(ADMM),sequential quadratic programming(SQP)and Armijo line search technique,we propose a novel monotone splitting SQP algorithm.First,the discussed problem is transformed into an optimization problem with only linear equality and box constraints by introduction of slack variables.Second,the idea of ADMM is used to decompose the traditional quadratic programming(QP)subproblem.In particular,the QP subproblem corresponding to the introduction of the slack variable is simple,and it has an explicit optimal solution without increasing the computational cost.Third,the search direction is generated by the optimal solutions of the subproblems,and the new iteration point is yielded by an Armijo line search with augmented Lagrange function.Fourth,the multiplier is updated by a novel approach that is different from the ADMM.Furthermore,the algorithm is extended to the associated optimization problem where the box constraints can be replaced by general nonempty closed convex sets.The global convergence of the two proposed algorithms is analyzed under weaker assumptions.Finally,some preliminary numerical experiments and applications in mid-to-large-scale economic dispatch problems for power systems are reported,and these show that the proposed algorithms are promising.展开更多
基金supported by the National Natural Science Foundation of China(12171106)the Natural Science Foundation of Guangxi Province(2020GXNSFDA238017 and 2018GXNSFFA281007)the Shanghai Sailing Program(21YF1430300)。
文摘This paper discusses the two-block large-scale nonconvex optimization problem with general linear constraints.Based on the ideas of splitting and sequential quadratic optimization(SQO),a new feasible descent method for the discussed problem is proposed.First,we consider the problem of quadratic optimal(QO)approximation associated with the current feasible iteration point,and we split the QO into two small-scale QOs which can be solved in parallel.Second,a feasible descent direction for the problem is obtained and a new SQO-type method is proposed,namely,splitting feasible SQO(SF-SQO)method.Moreover,under suitable conditions,we analyse the global convergence,strong convergence and rate of superlinear convergence of the SF-SQO method.Finally,preliminary numerical experiments regarding the economic dispatch of a power system are carried out,and these show that the SF-SQO method is promising.
基金supported by the National Natural Science Foundation of China(No.12261008)the Guangxi Natural Science Foundation(Nos.2023GXNSFAA026158 and 2020GXNSFDA238017)+1 种基金the Xiangsihu Young Scholars Innovative Research Team of Guangxi Minzu University(No.2022GXUNXSHQN04)the Guangxi Scholarship Fund of Guangxi Education Department(GED).
文摘This work discusses a class of two-block nonconvex optimization problems with linear equality,inequality and box constraints.Based on the ideas of alternating direction method with multipliers(ADMM),sequential quadratic programming(SQP)and Armijo line search technique,we propose a novel monotone splitting SQP algorithm.First,the discussed problem is transformed into an optimization problem with only linear equality and box constraints by introduction of slack variables.Second,the idea of ADMM is used to decompose the traditional quadratic programming(QP)subproblem.In particular,the QP subproblem corresponding to the introduction of the slack variable is simple,and it has an explicit optimal solution without increasing the computational cost.Third,the search direction is generated by the optimal solutions of the subproblems,and the new iteration point is yielded by an Armijo line search with augmented Lagrange function.Fourth,the multiplier is updated by a novel approach that is different from the ADMM.Furthermore,the algorithm is extended to the associated optimization problem where the box constraints can be replaced by general nonempty closed convex sets.The global convergence of the two proposed algorithms is analyzed under weaker assumptions.Finally,some preliminary numerical experiments and applications in mid-to-large-scale economic dispatch problems for power systems are reported,and these show that the proposed algorithms are promising.
