A global convergent algorithm is proposed to solve bilevel linear fractional-linear programming, which is a special class of bilevel programming. In our algorithm, replacing the lower level problem by its dual gap equ...A global convergent algorithm is proposed to solve bilevel linear fractional-linear programming, which is a special class of bilevel programming. In our algorithm, replacing the lower level problem by its dual gap equaling to zero, the bilevel linear fractional-linear programming is transformed into a traditional sin- gle level programming problem, which can be transformed into a series of linear fractional programming problem. Thus, the modi- fied convex simplex method is used to solve the infinite linear fractional programming to obtain the global convergent solution of the original bilevel linear fractional-linear programming. Finally, an example demonstrates the feasibility of the proposed algorithm.展开更多
Active set method and gradient projection method are curre nt ly the main approaches for linearly constrained convex programming. Interior-po int method is one of the most effective choices for linear programming. In ...Active set method and gradient projection method are curre nt ly the main approaches for linearly constrained convex programming. Interior-po int method is one of the most effective choices for linear programming. In the p aper a predictor-corrector interior-point algorithm for linearly constrained c onvex programming under the predictor-corrector motivation was proposed. In eac h iteration, the algorithm first performs a predictor-step to reduce the dualit y gap and then a corrector-step to keep the points close to the central traject ory. Computations in the algorithm only require that the initial iterate be nonn egative while feasibility or strict feasibility is not required. It is proved th at the algorithm is equivalent to a level-1 perturbed composite Newton method. Numerical experiments on twenty-six standard test problems are made. The result s show that the proposed algorithm is stable and robust.展开更多
With the expression theorem of convex polyhedron, this paper gives the general expression for the solutions in standard linear programming problems. And the calculation procedures in determining the optimal solutions ...With the expression theorem of convex polyhedron, this paper gives the general expression for the solutions in standard linear programming problems. And the calculation procedures in determining the optimal solutions are also given.展开更多
This paper deals with multiobjective programming problems with support functions under （G, C, ρ）-convexity assumptions. Not only sufficient but also necessary optimality conditions for this kind of multiobjective p...This paper deals with multiobjective programming problems with support functions under （G, C, ρ）-convexity assumptions. Not only sufficient but also necessary optimality conditions for this kind of multiobjective programming problems are established from a viewpoint of （G, C, ρ）-convexity. When the sufficient conditions are utilized, the corresponding duality theorems are derived for general Mond-Weir type dual program.展开更多
In this paper,an online midcourse guidance method for intercepting high-speed maneuvering targets is proposed.Firstly,the affine system is used to build a dynamic model and analyze the state constraints.The midcourse ...In this paper,an online midcourse guidance method for intercepting high-speed maneuvering targets is proposed.Firstly,the affine system is used to build a dynamic model and analyze the state constraints.The midcourse guidance problem is transformed into a continuous time optimization problem.Secondly,the problem is transformed into a discrete convex programming problem by affine control variable relaxation,Gaussian pseudospectral discretization and constraints linearization.Then,the off-line midcourse guidance trajectory is generated before midcourse guidance.It is used as the initial reference trajectory for online correction of midcourse guidance.An online guidance framework is used to eliminate the error caused by calculation of guidance instruction time.And the design of discrete points decreases with flight time to improve the solving efficiency.In addition,it is proposed that the terminal guidance capture is used innovatively space to judge the success of midcourse guidance.Numerical simulation shows the feasibility and effectiveness of the proposed method.展开更多
The traditional guidance law only guarantees the accuracy of attacking a target. However, the look angle and acceleration constraints are indispensable in applications. A new adaptive three-dimensional proportional na...The traditional guidance law only guarantees the accuracy of attacking a target. However, the look angle and acceleration constraints are indispensable in applications. A new adaptive three-dimensional proportional navigation(PN) guidance law is proposed based on convex optimization. Decomposition of the three-dimensional space is carried out to establish threedimensional kinematic engagements. The constraints and the performance index are disposed by using the convex optimization method. PN guidance gains can be obtained by solving the optimization problem. This solution is more rapid and programmatic than the traditional method and provides a foundation for future online guidance methods, which is of great value for engineering applications.展开更多
基金supported by the National Natural Science Foundation of China(70771080)the Special Fund for Basic Scientific Research of Central Colleges+2 种基金China University of Geosciences(Wuhan) (CUG090113)the Research Foundation for Outstanding Young TeachersChina University of Geosciences(Wuhan)(CUGQNW0801)
文摘A global convergent algorithm is proposed to solve bilevel linear fractional-linear programming, which is a special class of bilevel programming. In our algorithm, replacing the lower level problem by its dual gap equaling to zero, the bilevel linear fractional-linear programming is transformed into a traditional sin- gle level programming problem, which can be transformed into a series of linear fractional programming problem. Thus, the modi- fied convex simplex method is used to solve the infinite linear fractional programming to obtain the global convergent solution of the original bilevel linear fractional-linear programming. Finally, an example demonstrates the feasibility of the proposed algorithm.
文摘Active set method and gradient projection method are curre nt ly the main approaches for linearly constrained convex programming. Interior-po int method is one of the most effective choices for linear programming. In the p aper a predictor-corrector interior-point algorithm for linearly constrained c onvex programming under the predictor-corrector motivation was proposed. In eac h iteration, the algorithm first performs a predictor-step to reduce the dualit y gap and then a corrector-step to keep the points close to the central traject ory. Computations in the algorithm only require that the initial iterate be nonn egative while feasibility or strict feasibility is not required. It is proved th at the algorithm is equivalent to a level-1 perturbed composite Newton method. Numerical experiments on twenty-six standard test problems are made. The result s show that the proposed algorithm is stable and robust.
文摘With the expression theorem of convex polyhedron, this paper gives the general expression for the solutions in standard linear programming problems. And the calculation procedures in determining the optimal solutions are also given.
基金supported by the Natural Science Foundation of Guangdong Province under Grant No.S2013010013101the Science Foundations of Hanshan Normal University under Grant Nos.QD20131101and LZ201403
文摘This paper deals with multiobjective programming problems with support functions under （G, C, ρ）-convexity assumptions. Not only sufficient but also necessary optimality conditions for this kind of multiobjective programming problems are established from a viewpoint of （G, C, ρ）-convexity. When the sufficient conditions are utilized, the corresponding duality theorems are derived for general Mond-Weir type dual program.
文摘In this paper,an online midcourse guidance method for intercepting high-speed maneuvering targets is proposed.Firstly,the affine system is used to build a dynamic model and analyze the state constraints.The midcourse guidance problem is transformed into a continuous time optimization problem.Secondly,the problem is transformed into a discrete convex programming problem by affine control variable relaxation,Gaussian pseudospectral discretization and constraints linearization.Then,the off-line midcourse guidance trajectory is generated before midcourse guidance.It is used as the initial reference trajectory for online correction of midcourse guidance.An online guidance framework is used to eliminate the error caused by calculation of guidance instruction time.And the design of discrete points decreases with flight time to improve the solving efficiency.In addition,it is proposed that the terminal guidance capture is used innovatively space to judge the success of midcourse guidance.Numerical simulation shows the feasibility and effectiveness of the proposed method.
基金supported by the National Natural Science Foundation of China(61803357)。
文摘The traditional guidance law only guarantees the accuracy of attacking a target. However, the look angle and acceleration constraints are indispensable in applications. A new adaptive three-dimensional proportional navigation(PN) guidance law is proposed based on convex optimization. Decomposition of the three-dimensional space is carried out to establish threedimensional kinematic engagements. The constraints and the performance index are disposed by using the convex optimization method. PN guidance gains can be obtained by solving the optimization problem. This solution is more rapid and programmatic than the traditional method and provides a foundation for future online guidance methods, which is of great value for engineering applications.
