To reduce the number of the level sets used in algorithm of constrained nonlinear systems via ellipsoidal techniques, according to the analysis of mathematics, searching algorithm is used for choosing the control inpu...To reduce the number of the level sets used in algorithm of constrained nonlinear systems via ellipsoidal techniques, according to the analysis of mathematics, searching algorithm is used for choosing the control input. Simulation shows that the number of level sets used for controlling is almost the same as that used in polytope techniques. Sub time optimal algorithm reduces the number of the level sets used in ellipsoidal techniques.展开更多
This study proposes an efficient indirect approach for general nonlinear dynamic optimization problems without path constraints. The approach incorporates the virtues both from indirect and direct methods: it solves t...This study proposes an efficient indirect approach for general nonlinear dynamic optimization problems without path constraints. The approach incorporates the virtues both from indirect and direct methods: it solves the optimality conditions like the traditional indirect methods do, but uses a discretization technique inspired from direct methods. Compared with other indirect approaches, the proposed approach has two main advantages: (1) the discretized optimization problem only employs unconstrained nonlinear programming (NLP) algorithms such as BFGS (Broyden-Fletcher-Goldfarb-Shanno), rather than constrained NLP algorithms, therefore the computational efficiency is increased; (2) the relationship between the number of the discretized time intervals and the integration error of the four-step Adams predictor-corrector algorithm is established, thus the minimal number of time intervals that under desired integration tolerance can be estimated. The classic batch reactor problem is tested and compared in detail with literature reports, and the results reveal the effectiveness of the proposed approach. Dealing with path constraints requires extra techniques, and will be studied in the second paper.展开更多
This paper presents a new trust-region algorithm for general nonlinear constrained optimization problems. Certain equivalent KKT conditions of the problems are derived. Global convergence of the algorithm to a first-o...This paper presents a new trust-region algorithm for general nonlinear constrained optimization problems. Certain equivalent KKT conditions of the problems are derived. Global convergence of the algorithm to a first-order KKT point is established under mild conditions on the trial steps. Numerical example is also reported.展开更多
This paper proposes an arlene scaling derivative-free trust region method with interior backtracking technique for bounded-constrained nonlinear programming. This method is designed to get a stationary point for such ...This paper proposes an arlene scaling derivative-free trust region method with interior backtracking technique for bounded-constrained nonlinear programming. This method is designed to get a stationary point for such a problem with polynomial interpolation models instead of the objective function in trust region subproblem. Combined with both trust region strategy and line search technique, at each iteration, the affine scaling derivative-free trust region subproblem generates a backtracking direction in order to obtain a new accepted interior feasible step. Global convergence and fast local convergence properties are established under some reasonable conditions. Some numerical results are also given to show the effectiveness of the proposed algorithm.展开更多
A polyhedral active set algorithm PASA is developed for solving a nonlinear optimization problem whose feasible set is a polyhedron. Phase one of the algorithm is the gradient projection method, while phase two is any...A polyhedral active set algorithm PASA is developed for solving a nonlinear optimization problem whose feasible set is a polyhedron. Phase one of the algorithm is the gradient projection method, while phase two is any algorithm for solving a linearly constrained optimization problem. Rules are provided for branching between the two phases. Global convergence to a stationary point is established, while asymptotically PASA performs only phase two when either a nondegeneracy assumption holds, or the active constraints are linearly independent and a strong second-order sufficient optimality condition holds.展开更多
This paper proposes an inexact SQP method in association with line search filter technique for solving nonlinear equality constrained optimization. For large-scale applications, it is expensive to get an exact search ...This paper proposes an inexact SQP method in association with line search filter technique for solving nonlinear equality constrained optimization. For large-scale applications, it is expensive to get an exact search direction, and hence the authors use an inexact method that finds an approximate solution satisfying some appropriate conditions. The global convergence of the proposed algorithm is established by using line search filter technique. The second-order correction step is used to overcome the Maratos effect, while the line search filter inexact SQP method has q-superlinear local convergence rate. Finally, the results of numerical experiments indicate that the proposed method is efficient for the given test problems.展开更多
Inflatable membrane antennas have been extensively applied in space missions;however,the simulation methods are not perfect,and many simulation methods still have many difficulties in accuracy,efficiency,and stability...Inflatable membrane antennas have been extensively applied in space missions;however,the simulation methods are not perfect,and many simulation methods still have many difficulties in accuracy,efficiency,and stability.Therefore,the extended position-based dynamics(XPBD)method is employed and improved for the simulation of folded inflatable structures in this paper.To overcome the problem that the original XPBD method with only geometric constraints does not contain any mechanical information and cannot reflect the mechanical characteristics of the structure,we improve the XPBD method by introducing the strain energy constraint.Due to the complicated nonlinear characteristics of the membrane structures,the results with the traditional finite element method(Abaqus)cannot converge,while the tension field theory(TFT)can,but some pretreatments are needed.Compared with them,the method in this paper is simple and has better stability to accurately predict the displacement,stress,and wrinkle region of the membrane structure.In addition,the present method is also compared with the experiment in the reference to verify the feasibility of the folded tube simulation.Finally,the present method is applied to simulate inflatable membrane antennas and analyze the deployable driving force and deployable process sequence of each component.展开更多
文摘To reduce the number of the level sets used in algorithm of constrained nonlinear systems via ellipsoidal techniques, according to the analysis of mathematics, searching algorithm is used for choosing the control input. Simulation shows that the number of level sets used for controlling is almost the same as that used in polytope techniques. Sub time optimal algorithm reduces the number of the level sets used in ellipsoidal techniques.
基金Supported by the National Natural Science Foundation of China (U1162130)the National High Technology Research and Development Program of China (2006AA05Z226)the Outstanding Youth Science Foundation,Zhejiang Province (R4100133)
文摘This study proposes an efficient indirect approach for general nonlinear dynamic optimization problems without path constraints. The approach incorporates the virtues both from indirect and direct methods: it solves the optimality conditions like the traditional indirect methods do, but uses a discretization technique inspired from direct methods. Compared with other indirect approaches, the proposed approach has two main advantages: (1) the discretized optimization problem only employs unconstrained nonlinear programming (NLP) algorithms such as BFGS (Broyden-Fletcher-Goldfarb-Shanno), rather than constrained NLP algorithms, therefore the computational efficiency is increased; (2) the relationship between the number of the discretized time intervals and the integration error of the four-step Adams predictor-corrector algorithm is established, thus the minimal number of time intervals that under desired integration tolerance can be estimated. The classic batch reactor problem is tested and compared in detail with literature reports, and the results reveal the effectiveness of the proposed approach. Dealing with path constraints requires extra techniques, and will be studied in the second paper.
基金Supported by the Scientific Research Foundation of Hunan Provincial Education Department(02B021) Hunan Provincial Natural Science Foundation,China(03JJY6002)
文摘This paper presents a new trust-region algorithm for general nonlinear constrained optimization problems. Certain equivalent KKT conditions of the problems are derived. Global convergence of the algorithm to a first-order KKT point is established under mild conditions on the trial steps. Numerical example is also reported.
基金supported by the National Science Foundation of China under Grant No.11371253
文摘This paper proposes an arlene scaling derivative-free trust region method with interior backtracking technique for bounded-constrained nonlinear programming. This method is designed to get a stationary point for such a problem with polynomial interpolation models instead of the objective function in trust region subproblem. Combined with both trust region strategy and line search technique, at each iteration, the affine scaling derivative-free trust region subproblem generates a backtracking direction in order to obtain a new accepted interior feasible step. Global convergence and fast local convergence properties are established under some reasonable conditions. Some numerical results are also given to show the effectiveness of the proposed algorithm.
基金supported by the National Science Foundation of USA(Grant Nos.1522629 and 1522654)the Office of Naval Research of USA(Grant Nos.N00014-11-1-0068 and N00014-15-12048)+1 种基金the Air Force Research Laboratory of USA(Contract No.FA8651-08-D-0108/0054)National Natural Science Foundation of China(Grant No.11571178)
文摘A polyhedral active set algorithm PASA is developed for solving a nonlinear optimization problem whose feasible set is a polyhedron. Phase one of the algorithm is the gradient projection method, while phase two is any algorithm for solving a linearly constrained optimization problem. Rules are provided for branching between the two phases. Global convergence to a stationary point is established, while asymptotically PASA performs only phase two when either a nondegeneracy assumption holds, or the active constraints are linearly independent and a strong second-order sufficient optimality condition holds.
基金supported by the National Science Foundation Grant under Grant No.10871130the Shanghai Leading Academic Discipline Project under Grant No.T0401
文摘This paper proposes an inexact SQP method in association with line search filter technique for solving nonlinear equality constrained optimization. For large-scale applications, it is expensive to get an exact search direction, and hence the authors use an inexact method that finds an approximate solution satisfying some appropriate conditions. The global convergence of the proposed algorithm is established by using line search filter technique. The second-order correction step is used to overcome the Maratos effect, while the line search filter inexact SQP method has q-superlinear local convergence rate. Finally, the results of numerical experiments indicate that the proposed method is efficient for the given test problems.
基金supported by the National Natural Science Foundation of China(Grant Nos.11922203 and 11772074).
文摘Inflatable membrane antennas have been extensively applied in space missions;however,the simulation methods are not perfect,and many simulation methods still have many difficulties in accuracy,efficiency,and stability.Therefore,the extended position-based dynamics(XPBD)method is employed and improved for the simulation of folded inflatable structures in this paper.To overcome the problem that the original XPBD method with only geometric constraints does not contain any mechanical information and cannot reflect the mechanical characteristics of the structure,we improve the XPBD method by introducing the strain energy constraint.Due to the complicated nonlinear characteristics of the membrane structures,the results with the traditional finite element method(Abaqus)cannot converge,while the tension field theory(TFT)can,but some pretreatments are needed.Compared with them,the method in this paper is simple and has better stability to accurately predict the displacement,stress,and wrinkle region of the membrane structure.In addition,the present method is also compared with the experiment in the reference to verify the feasibility of the folded tube simulation.Finally,the present method is applied to simulate inflatable membrane antennas and analyze the deployable driving force and deployable process sequence of each component.
