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
Although QP-free algorithms have good theoretical convergence and are effective in practice,their applications to minimax optimization have not yet been investigated.In this article,on the basis of the stationary cond...Although QP-free algorithms have good theoretical convergence and are effective in practice,their applications to minimax optimization have not yet been investigated.In this article,on the basis of the stationary conditions,without the exponential smooth function or constrained smooth transformation,we propose a QP-free algorithm for the nonlinear minimax optimization with inequality constraints.By means of a new and much tighter working set,we develop a new technique for constructing the sub-matrix in the lower right corner of the coefficient matrix.At each iteration,to obtain the search direction,two reduced systems of linear equations with the same coefficient are solved.Under mild conditions,the proposed algorithm is globally convergent.Finally,some preliminary numerical experiments are reported,and these show that the algorithm is promising.展开更多
In this paper,we discuss the nonlinear minimax problems with inequality constraints.Based on the stationary conditions of the discussed problems,we propose a sequential systems of linear equations(SSLE)-type algorithm...In this paper,we discuss the nonlinear minimax problems with inequality constraints.Based on the stationary conditions of the discussed problems,we propose a sequential systems of linear equations(SSLE)-type algorithm of quasi-strongly sub-feasible directions with an arbitrary initial iteration point.By means of the new working set,we develop a new technique for constructing the sub-matrix in the lower right corner of the coefficient matrix of the system of linear equations(SLE).At each iteration,two systems of linear equations(SLEs)with the same uniformly nonsingular coefficient matrix are solved.Under mild conditions,the proposed algorithm possesses global and strong convergence.Finally,some preliminary numerical experiments are reported.展开更多
In this paper,the nonlinear optimization problems with inequality constraints are discussed. Combining the ideas of the strongly sub-feasible directions method and theε-generalized projection technique,a new algorith...In this paper,the nonlinear optimization problems with inequality constraints are discussed. Combining the ideas of the strongly sub-feasible directions method and theε-generalized projection technique,a new algorithm starting with an arbitrary initial iteration point for the discussed problems is presented.At each iteration,the search direction is generated by a new ?-generalized projection explicit formula,and the step length is yielded by a new Armijo line search.Under some necessary assumptions, not only the algorithm possesses global and strong convergence,but also the iterative points always get into the feasible set after finite iterations.Finally,some preliminary numerical results are reported.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the Natural Science Foundation of Guangxi Province(2018GXNSFAA281099)the National Natural Science Foundation of China(11771383)the Yulin Normal University Research Grant(2019YJKY16).
文摘Although QP-free algorithms have good theoretical convergence and are effective in practice,their applications to minimax optimization have not yet been investigated.In this article,on the basis of the stationary conditions,without the exponential smooth function or constrained smooth transformation,we propose a QP-free algorithm for the nonlinear minimax optimization with inequality constraints.By means of a new and much tighter working set,we develop a new technique for constructing the sub-matrix in the lower right corner of the coefficient matrix.At each iteration,to obtain the search direction,two reduced systems of linear equations with the same coefficient are solved.Under mild conditions,the proposed algorithm is globally convergent.Finally,some preliminary numerical experiments are reported,and these show that the algorithm is promising.
基金supported by the Research Foundation of Guangxi University for Nationalities(No.2021KJQD04)the Natural Science Foundation of Guangxi Province(No.2018GXNSFAA281099)and NSFC(No.11771383).
文摘In this paper,we discuss the nonlinear minimax problems with inequality constraints.Based on the stationary conditions of the discussed problems,we propose a sequential systems of linear equations(SSLE)-type algorithm of quasi-strongly sub-feasible directions with an arbitrary initial iteration point.By means of the new working set,we develop a new technique for constructing the sub-matrix in the lower right corner of the coefficient matrix of the system of linear equations(SLE).At each iteration,two systems of linear equations(SLEs)with the same uniformly nonsingular coefficient matrix are solved.Under mild conditions,the proposed algorithm possesses global and strong convergence.Finally,some preliminary numerical experiments are reported.
基金supported by the National Natural Science Foundation of China under Grant Nos.71061002 and 10771040the Project supported by Guangxi Science Foundation under Grant No.0832052Science Foundation of Guangxi Education Department under Grant No.200911MS202
文摘In this paper,the nonlinear optimization problems with inequality constraints are discussed. Combining the ideas of the strongly sub-feasible directions method and theε-generalized projection technique,a new algorithm starting with an arbitrary initial iteration point for the discussed problems is presented.At each iteration,the search direction is generated by a new ?-generalized projection explicit formula,and the step length is yielded by a new Armijo line search.Under some necessary assumptions, not only the algorithm possesses global and strong convergence,but also the iterative points always get into the feasible set after finite iterations.Finally,some preliminary numerical results are reported.
