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
In this paper, a new mixed quasi-Newton method for inequality constrained optimization problems is proposed. The feature of the method is that only the systems of linear equations are solved in each iteration, other t...In this paper, a new mixed quasi-Newton method for inequality constrained optimization problems is proposed. The feature of the method is that only the systems of linear equations are solved in each iteration, other than the quadratic programming, which decrease the amount of computations and is also efficient for large scale problem. Under some mild assumptions without the strict complementary condition., the method is globally and superlinearly convergent.展开更多
In this paper, a new trust region algorithm for nonlinear equality constrained LC1 optimization problems is given. It obtains a search direction at each iteration not by solving a quadratic programming subprobiem with...In this paper, a new trust region algorithm for nonlinear equality constrained LC1 optimization problems is given. It obtains a search direction at each iteration not by solving a quadratic programming subprobiem with a trust region bound, but by solving a system of linear equations. Since the computational complexity of a QP-Problem is in general much larger than that of a system of linear equations, this method proposed in this paper may reduce the computational complexity and hence improve computational efficiency. Furthermore, it is proved under appropriate assumptions that this algorithm is globally and super-linearly convergent to a solution of the original problem. Some numerical examples are reported, showing the proposed algorithm can be beneficial from a computational point of view.展开更多
A new trust region algorithm for solving convex LC 1 optimization problem is presented.It is proved that the algorithm is globally convergent and the rate of convergence is superlinear under some reasonable assum...A new trust region algorithm for solving convex LC 1 optimization problem is presented.It is proved that the algorithm is globally convergent and the rate of convergence is superlinear under some reasonable assumptions.展开更多
A noninterior continuation method is proposed for semidefinite complementarity problem （SDCP）. This method improves the noninterior continuation methods recently developed for SDCP by Chen and Tseng. The main proper...A noninterior continuation method is proposed for semidefinite complementarity problem （SDCP）. This method improves the noninterior continuation methods recently developed for SDCP by Chen and Tseng. The main properties of our method are： （i） it is well d.efined for the monotones SDCP; （ii） it has to solve just one linear system of equations at each step; （iii） it is shown to be both globally linearly convergent and locally quadratically convergent under suitable assumptions.展开更多
The present paper is devoted to a novel smoothing function method for convex quadratic programming problem with mixed constrains, which has important application in mechanics and engineering science. The problem is re...The present paper is devoted to a novel smoothing function method for convex quadratic programming problem with mixed constrains, which has important application in mechanics and engineering science. The problem is reformulated as a system of non-smooth equations, and then a smoothing function for the system of non-smooth equations is proposed. The condition of convergences of this iteration algorithm is given. Theory analysis and primary numerical results illustrate that this method is feasible and effective.展开更多
In this paper, a new globally convergent algorithm for nonlinear optimization problems with equality and inequality constraints is presented. The new algorithm is of SQP type which determines a search direction by sol...In this paper, a new globally convergent algorithm for nonlinear optimization problems with equality and inequality constraints is presented. The new algorithm is of SQP type which determines a search direction by solving a quadratic programming subproblem per iteration. Some revisions on the quadratic programming subproblem have been made in such a way that the associated constraint region is nonempty for each point x generated by the algorithm, i.e. , the subproblems always have optimal solutions. The new algorithm has two important properties. The computation of revision parameter for guaranteeing the consistency of quadratic subproblem and the computation of the second order correction step for superlinear convergence use the same inverse of a matrix per iteration, so the computation amount of the new algorithm will not be increased much more than other SQP type algorithms; Another is that the new algorithm can give automatically a feasible point as a starting point for the quadratic subproblems per iteration, this will obivously simplify the computation procedure of the subproblems. Some numerical results are reported.展开更多
In this paper, by using a new projection, we construct a variant of Zhang’s algorithm and prove its convergence. Specially, the variant of Zhang’s algorithm has quadratic termination and superlinear convergence rale...In this paper, by using a new projection, we construct a variant of Zhang’s algorithm and prove its convergence. Specially, the variant of Zhang’s algorithm has quadratic termination and superlinear convergence rale under certain conditions. Zhang’s algorithm hasn’t these properties.展开更多
According to the sequential BFGS method, in this paper we present an asynchronous parallel BFGS method in the case when the gradient information about the function is inexact. We assume that we have p + q processors, ...According to the sequential BFGS method, in this paper we present an asynchronous parallel BFGS method in the case when the gradient information about the function is inexact. We assume that we have p + q processors, which are divided-into two groups, the first group has p processors, the second group has q processors, the two groups are asynchronous. parallel, If we assume the objective function is twice continuously differentiable and uniformly convex, we prove the iteration converge globally to the solution, and under some additional conditions we show the method is superlinearly convergent. Finally, we show the numerical results of this algorithm.展开更多
A one_step smoothing Newton method is proposed for solving the vertical linear complementarity problem based on the so_called aggregation function. The proposed algorithm has the following good features: (ⅰ) It solve...A one_step smoothing Newton method is proposed for solving the vertical linear complementarity problem based on the so_called aggregation function. The proposed algorithm has the following good features: (ⅰ) It solves only one linear system of equations and does only one line search at each iteration; (ⅱ) It is well_defined for the vertical linear complementarity problem with vertical block P 0 matrix and any accumulation point of iteration sequence is its solution.Moreover, the iteration sequence is bounded for the vertical linear complementarity problem with vertical block P 0+R 0 matrix; (ⅲ) It has both global linear and local quadratic convergence without strict complementarity. Many existing smoothing Newton methods do not have the property (ⅲ).展开更多
We propose a stochastic level value approximation method for a quadratic integer convex minimizing problem in this paper. This method applies an importance sampling technique, and make use of the cross-entropy method ...We propose a stochastic level value approximation method for a quadratic integer convex minimizing problem in this paper. This method applies an importance sampling technique, and make use of the cross-entropy method to update the sample density functions. We also prove the asymptotic convergence of this algorithm, and report some numerical results to illuminate its effectiveness.展开更多
In this paper we prove that a class of trust region methods presented in part I is superlinearly convergent. Numerical tests are reported thereafter. Results by solving a set of typical problems selected from literatu...In this paper we prove that a class of trust region methods presented in part I is superlinearly convergent. Numerical tests are reported thereafter. Results by solving a set of typical problems selected from literatures have demonstrated that our algorithm is effective.展开更多
In this paper, a new trust region algorithm for unconstrained LC1 optimization problems is given. Compare with those existing trust regiion methods, this algorithm has a different feature: it obtains a stepsize at eac...In this paper, a new trust region algorithm for unconstrained LC1 optimization problems is given. Compare with those existing trust regiion methods, this algorithm has a different feature: it obtains a stepsize at each iteration not by soloving a quadratic subproblem with a trust region bound, but by solving a system of linear equations. Thus it reduces computational complexity and improves computation efficiency. It is proven that this algorithm is globally convergent and locally superlinear under some conditions.展开更多
A noninterior continuation method is presented, with only the certering step used at each iteration, for nonlinear complementarity problem. It is shown that the algorithm is globally linearly and locally quadratically...A noninterior continuation method is presented, with only the certering step used at each iteration, for nonlinear complementarity problem. It is shown that the algorithm is globally linearly and locally quadratically convergent under certain conditions.展开更多
This paper presents a quadratically approximate algorithm framework （QAAF） for solving general constrained optimization problems, which solves, at each iteration, a subproblem with quadratic objective function and q...This paper presents a quadratically approximate algorithm framework （QAAF） for solving general constrained optimization problems, which solves, at each iteration, a subproblem with quadratic objective function and quadratic equality together with inequality constraints. The global convergence of the algorithm framework is presented under the Mangasarian-Fromovitz constraint qualification （MFCQ）, and the conditions for superlinear and quadratic convergence of the algorithm framework are given under the MFCQ, the constant rank constraint qualification （CRCQ） as well as the strong second-order sufficiency conditions （SSOSC）. As an incidental result, the definition of an approximate KKT point is brought forward, and the global convergence of a sequence of approximate KKT points is analysed.展开更多
We propose a one–step smoothing Newton method for solving the non-linearcomplementarity problem with P 0–function (P_0–NCP) based on the smoothing symmetric perturbedFisher function (for short, denoted as the SSPF...We propose a one–step smoothing Newton method for solving the non-linearcomplementarity problem with P 0–function (P_0–NCP) based on the smoothing symmetric perturbedFisher function (for short, denoted as the SSPF–function). The proposed algorithm has to solve onlyone linear system of equations and performs only one line search per iteration. Without requiringany strict complementarity assumption at the P_0–NCP solution, we show that the proposed algorithmconverges globally and superlinearly under mild conditions. Furthermore, the algorithm has localquadratic convergence under suitable conditions. The main feature of our global convergence resultsis that we do not assume a priori the existence of an accumulation point. Compared to the previousliteratures, our algorithm has stronger convergence results under weaker conditions.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.
文摘In this paper, a new mixed quasi-Newton method for inequality constrained optimization problems is proposed. The feature of the method is that only the systems of linear equations are solved in each iteration, other than the quadratic programming, which decrease the amount of computations and is also efficient for large scale problem. Under some mild assumptions without the strict complementary condition., the method is globally and superlinearly convergent.
文摘In this paper, a new trust region algorithm for nonlinear equality constrained LC1 optimization problems is given. It obtains a search direction at each iteration not by solving a quadratic programming subprobiem with a trust region bound, but by solving a system of linear equations. Since the computational complexity of a QP-Problem is in general much larger than that of a system of linear equations, this method proposed in this paper may reduce the computational complexity and hence improve computational efficiency. Furthermore, it is proved under appropriate assumptions that this algorithm is globally and super-linearly convergent to a solution of the original problem. Some numerical examples are reported, showing the proposed algorithm can be beneficial from a computational point of view.
基金Supported by the National Natural Science Foundation of P.R.China(1 9971 0 0 2 ) and the Subject ofBeijing Educational Committ
文摘A new trust region algorithm for solving convex LC 1 optimization problem is presented.It is proved that the algorithm is globally convergent and the rate of convergence is superlinear under some reasonable assumptions.
基金This work was supported by the National Natural Science Foundation of China (10201001, 70471008)
文摘A noninterior continuation method is proposed for semidefinite complementarity problem （SDCP）. This method improves the noninterior continuation methods recently developed for SDCP by Chen and Tseng. The main properties of our method are： （i） it is well d.efined for the monotones SDCP; （ii） it has to solve just one linear system of equations at each step; （iii） it is shown to be both globally linearly convergent and locally quadratically convergent under suitable assumptions.
文摘The present paper is devoted to a novel smoothing function method for convex quadratic programming problem with mixed constrains, which has important application in mechanics and engineering science. The problem is reformulated as a system of non-smooth equations, and then a smoothing function for the system of non-smooth equations is proposed. The condition of convergences of this iteration algorithm is given. Theory analysis and primary numerical results illustrate that this method is feasible and effective.
基金This research was supported by the National Natural Science Foundation of China and the Natural Science Foundation of Shandong Province.
文摘In this paper, a new globally convergent algorithm for nonlinear optimization problems with equality and inequality constraints is presented. The new algorithm is of SQP type which determines a search direction by solving a quadratic programming subproblem per iteration. Some revisions on the quadratic programming subproblem have been made in such a way that the associated constraint region is nonempty for each point x generated by the algorithm, i.e. , the subproblems always have optimal solutions. The new algorithm has two important properties. The computation of revision parameter for guaranteeing the consistency of quadratic subproblem and the computation of the second order correction step for superlinear convergence use the same inverse of a matrix per iteration, so the computation amount of the new algorithm will not be increased much more than other SQP type algorithms; Another is that the new algorithm can give automatically a feasible point as a starting point for the quadratic subproblems per iteration, this will obivously simplify the computation procedure of the subproblems. Some numerical results are reported.
基金The subject is supported by Natural Science Foundation of China and Natural Science Foundation of Shandong Province.
文摘In this paper, by using a new projection, we construct a variant of Zhang’s algorithm and prove its convergence. Specially, the variant of Zhang’s algorithm has quadratic termination and superlinear convergence rale under certain conditions. Zhang’s algorithm hasn’t these properties.
文摘According to the sequential BFGS method, in this paper we present an asynchronous parallel BFGS method in the case when the gradient information about the function is inexact. We assume that we have p + q processors, which are divided-into two groups, the first group has p processors, the second group has q processors, the two groups are asynchronous. parallel, If we assume the objective function is twice continuously differentiable and uniformly convex, we prove the iteration converge globally to the solution, and under some additional conditions we show the method is superlinearly convergent. Finally, we show the numerical results of this algorithm.
文摘A one_step smoothing Newton method is proposed for solving the vertical linear complementarity problem based on the so_called aggregation function. The proposed algorithm has the following good features: (ⅰ) It solves only one linear system of equations and does only one line search at each iteration; (ⅱ) It is well_defined for the vertical linear complementarity problem with vertical block P 0 matrix and any accumulation point of iteration sequence is its solution.Moreover, the iteration sequence is bounded for the vertical linear complementarity problem with vertical block P 0+R 0 matrix; (ⅲ) It has both global linear and local quadratic convergence without strict complementarity. Many existing smoothing Newton methods do not have the property (ⅲ).
基金Project supported by the National Natural Science Foundation of China (No.10671117)Shanghai Leading Academic Discipline Project (No.J050101)the Youth Science Foundation of Hunan Education Department of China (No.06B037)
文摘We propose a stochastic level value approximation method for a quadratic integer convex minimizing problem in this paper. This method applies an importance sampling technique, and make use of the cross-entropy method to update the sample density functions. We also prove the asymptotic convergence of this algorithm, and report some numerical results to illuminate its effectiveness.
文摘In this paper we prove that a class of trust region methods presented in part I is superlinearly convergent. Numerical tests are reported thereafter. Results by solving a set of typical problems selected from literatures have demonstrated that our algorithm is effective.
文摘In this paper, a new trust region algorithm for unconstrained LC1 optimization problems is given. Compare with those existing trust regiion methods, this algorithm has a different feature: it obtains a stepsize at each iteration not by soloving a quadratic subproblem with a trust region bound, but by solving a system of linear equations. Thus it reduces computational complexity and improves computation efficiency. It is proven that this algorithm is globally convergent and locally superlinear under some conditions.
文摘A noninterior continuation method is presented, with only the certering step used at each iteration, for nonlinear complementarity problem. It is shown that the algorithm is globally linearly and locally quadratically convergent under certain conditions.
基金NSFC (Nos.10261001,10771040)Guangxi Province Science Foundation (No.0640001)
文摘This paper presents a quadratically approximate algorithm framework （QAAF） for solving general constrained optimization problems, which solves, at each iteration, a subproblem with quadratic objective function and quadratic equality together with inequality constraints. The global convergence of the algorithm framework is presented under the Mangasarian-Fromovitz constraint qualification （MFCQ）, and the conditions for superlinear and quadratic convergence of the algorithm framework are given under the MFCQ, the constant rank constraint qualification （CRCQ） as well as the strong second-order sufficiency conditions （SSOSC）. As an incidental result, the definition of an approximate KKT point is brought forward, and the global convergence of a sequence of approximate KKT points is analysed.
基金This work is partly supported by the National Natural Science Foundation of China(Grant,Nos.10271002,10201001)
文摘We propose a one–step smoothing Newton method for solving the non-linearcomplementarity problem with P 0–function (P_0–NCP) based on the smoothing symmetric perturbedFisher function (for short, denoted as the SSPF–function). The proposed algorithm has to solve onlyone linear system of equations and performs only one line search per iteration. Without requiringany strict complementarity assumption at the P_0–NCP solution, we show that the proposed algorithmconverges globally and superlinearly under mild conditions. Furthermore, the algorithm has localquadratic convergence under suitable conditions. The main feature of our global convergence resultsis that we do not assume a priori the existence of an accumulation point. Compared to the previousliteratures, our algorithm has stronger convergence results under weaker conditions.
