Generating dynamically feasible trajectory for fixed-wing Unmanned Aerial Vehicles(UAVs)in dense obstacle environments remains computationally intractable.This paper proposes a Safe Flight Corridor constrained Sequent...Generating dynamically feasible trajectory for fixed-wing Unmanned Aerial Vehicles(UAVs)in dense obstacle environments remains computationally intractable.This paper proposes a Safe Flight Corridor constrained Sequential Convex Programming(SFC-SCP)to improve the computation efficiency and reliability of trajectory generation.SFC-SCP combines the front-end convex polyhedron SFC construction and back-end SCP-based trajectory optimization.A Sparse A^(*)Search(SAS)driven SFC construction method is designed to efficiently generate polyhedron SFC according to the geometric relation among obstacles and collision-free waypoints.Via transforming the nonconvex obstacle-avoidance constraints to linear inequality constraints,SFC can mitigate infeasibility of trajectory planning and reduce computation complexity.Then,SCP casts the nonlinear trajectory optimization subject to SFC into convex programming subproblems to decrease the problem complexity.In addition,a convex optimizer based on interior point method is customized,where the search direction is calculated via successive elimination to further improve efficiency.Simulation experiments on dense obstacle scenarios show that SFC-SCP can generate dynamically feasible safe trajectory rapidly.Comparative studies with state-of-the-art SCP-based methods demonstrate the efficiency and reliability merits of SFC-SCP.Besides,the customized convex optimizer outperforms off-the-shelf optimizers in terms of computation time.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
The detection of sparse signals against background noise is considered. Detecting signals of such kind is difficult since only a small portion of the signal carries information. Prior knowledge is usually assumed to e...The detection of sparse signals against background noise is considered. Detecting signals of such kind is difficult since only a small portion of the signal carries information. Prior knowledge is usually assumed to ease detection. In this paper, we consider the general unknown and arbitrary sparse signal detection problem when no prior knowledge is available. Under a Ney- man-Pearson hypothesis-testing framework, a new detection scheme is proposed by combining a generalized likelihood ratio test （GLRT）-Iike test statistic and convex programming methods which directly exploit sparsity in an underdetermined system of linear equations. We characterize large sample behavior of the proposed method by analyzing its asymptotic performance. Specifically, we give the condition for the Chernoff-consistent detection which shows that the proposed method is very sensitive to the norm energy of the sparse signals. Both the false alam rate and the miss rate tend to zero at vanishing signal-to-noise ratio （SNR）, as long as the signal energy grows at least logarithmically with the problem dimension. Next we give a large deviation analysis to characterize the error exponent for the Neyman-Pearson detection. We derive the oracle error exponent assuming signal knowledge. Then we explicitly derive the error exponent of the proposed scheme and compare it with the oracle exponent. We complement our study with numerical experiments, showing that the proposed method performs in the vicinity of the likelihood ratio test （LRT） method in the finite sample scenario and the error probability degrades exponentially with the number of observations.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
A potential reduction algorithm is proposed for optimization of a convex function subject to linear constraints.At each step of the algorithm,a system of linear equations is solved to get a search direction and the Ar...A potential reduction algorithm is proposed for optimization of a convex function subject to linear constraints.At each step of the algorithm,a system of linear equations is solved to get a search direction and the Armijo's rule is used to determine a stepsize.It is proved that the algorithm is globally convergent.Computational results are reported.展开更多
An algorithm for solving a class of smooth convex programming is given. Using smooth exact multiplier penalty function, a smooth convex programming is minimized to a minimizing strongly convex function on the compact ...An algorithm for solving a class of smooth convex programming is given. Using smooth exact multiplier penalty function, a smooth convex programming is minimized to a minimizing strongly convex function on the compact set was reduced. Then the strongly convex function with a Newton method on the given compact set was minimized.展开更多
In this paper,we present two parallel multiplicative algorithms for convex programming.If the objective function has compact level sets and has a locally Lipschitz continuous gradient,we discuss convergence of the alg...In this paper,we present two parallel multiplicative algorithms for convex programming.If the objective function has compact level sets and has a locally Lipschitz continuous gradient,we discuss convergence of the algorithms.The proofs are essentially based on the results of sequential methods shown by Eggermontt[1].展开更多
In this paper, we establish the second-order differential equation system with the feedback controls for solving the problem of convex programming. Using Lagrange function and projection operator, the equivalent opera...In this paper, we establish the second-order differential equation system with the feedback controls for solving the problem of convex programming. Using Lagrange function and projection operator, the equivalent operator equations for the convex programming problems under the certain conditions are obtained. Then a second-order differential equation system with the feedback controls is constructed on the basis of operator equation. We prove that any accumulation point of the trajectory of the second-order differential equation system with the feedback controls is a solution to the convex programming problem. In the end, two examples using this differential equation system are solved. The numerical results are reported to verify the effectiveness of the second-order differential equation system with the feedback controls for solving the convex programming problem.展开更多
With the rapid changes of the flight environment and situation,there will be various unexpected situations while multiple missiles are performing the missions.To fast cope with the various situations in mission execut...With the rapid changes of the flight environment and situation,there will be various unexpected situations while multiple missiles are performing the missions.To fast cope with the various situations in mission executions,the conventional sequential convex programming algorithm and the parallel-based sequential convex programming algorithm for multiple missiles fast trajectory replanning are proposed in this paper.The originally non-convex trajectory optimization problem is reformulated into a series of convex optimization subproblems based on the sequential convex programming method.The conventional sequential convex programming algorithm is developed through linearization,successive convexification,and relaxation techniques to solve the convex optimization subproblems iteratively.However,multiple missiles are related through various cooperative constraints.When the trajectory optimization of multiple missiles is formulated as an optimal control problem to solve,the complexity of the problem will increase dramatically as the number of missiles increases.To alleviate the coupled effect caused by multiple aerodynamically controlled missiles,the parallel-based sequential convex programming algorithm is proposed to solve the trajectory optimization problem for multiple missiles in parallel,reducing the complexity of the trajectory optimization problem and significantly shortening the computation time.Numerical simulations are provided to verify the convergence and effectiveness of the conventional sequential convex programming algorithm and the parallel-based sequential convex programming algorithm to cope with the trajectory optimization problem with various constraints.Furthermore,the optimality and the real-time performance of the proposed algorithms are discussed in comparative simulation examples.展开更多
A class of functions and a sort of nonlinear programming called respectively E-convex functions and E-convex programming were presented and studied recently by Youness in [1], In this paper, we point out the most resu...A class of functions and a sort of nonlinear programming called respectively E-convex functions and E-convex programming were presented and studied recently by Youness in [1], In this paper, we point out the most results for .E-convex functions and E-convex programming in [1] are not true by six counter examples.展开更多
In this paper, we describe a method to solve large-scale structural optimization problems by sequential convex programming （SCP）. A predictor-corrector interior point method is applied to solve the strictly convex s...In this paper, we describe a method to solve large-scale structural optimization problems by sequential convex programming （SCP）. A predictor-corrector interior point method is applied to solve the strictly convex subproblems. The SCP algorithm and the topology optimization approach are introduced. Especially, different strategies to solve certain linear systems of equations are analyzed. Numerical results are presented to show the efficiency of the proposed method for solving topology optimization problems and to compare different variants.展开更多
The strictly contractive Peaceman-Rachford splitting method is one of effective methods for solving separable convex optimization problem, and the inertial proximal Peaceman-Rachford splitting method is one of its imp...The strictly contractive Peaceman-Rachford splitting method is one of effective methods for solving separable convex optimization problem, and the inertial proximal Peaceman-Rachford splitting method is one of its important variants. It is known that the convergence of the inertial proximal Peaceman- Rachford splitting method can be ensured if the relaxation factor in Lagrangian multiplier updates is underdetermined, which means that the steps for the Lagrangian multiplier updates are shrunk conservatively. Although small steps play an important role in ensuring convergence, they should be strongly avoided in practice. In this article, we propose a relaxed inertial proximal Peaceman- Rachford splitting method, which has a larger feasible set for the relaxation factor. Thus, our method provides the possibility to admit larger steps in the Lagrangian multiplier updates. We establish the global convergence of the proposed algorithm under the same conditions as the inertial proximal Peaceman-Rachford splitting method. Numerical experimental results on a sparse signal recovery problem in compressive sensing and a total variation based image denoising problem demonstrate the effectiveness of our method.展开更多
This paper gives a new dual problem for nondifferentiable convex programming and provesthe properties of weak duality and strong duality and offers a necessary and sufficient condition ofstrong duality.
It has been shown that the alternating direction method of multipliers(ADMM)is not necessarily convergent when it is directly extended to a multiple-block linearly constrained convex minimization model with an objecti...It has been shown that the alternating direction method of multipliers(ADMM)is not necessarily convergent when it is directly extended to a multiple-block linearly constrained convex minimization model with an objective function that is in the sum of more than two functions without coupled variables.Recently,we pro-posed the block-wise ADMM,which was obtained by regrouping the variables and functions of such a model as two blocks and then applying the original ADMM in block-wise.This note is a further study on this topic with the purpose of showing that a well-known relaxation factor proposed by Fortin and Glowinski for iteratively updat-ing the Lagrangian multiplier of the originalADMMcan also be used in the block-wise ADMM.We thus propose the block-wise ADMM with Fortin and Glowinski’s relax-ation factor for the multiple-block convex minimization model.Like the block-wise ADMM,we also suggest further decomposing the resulting subproblems and regular-izing them by proximal terms to ensure the convergence.For the block-wise ADMM with Fortin and Glowinski's relaxation factor,its convergence and worst-case conver-gence rate measured by the iteration complexity in the ergodic sense are derived.展开更多
This article presents a polynomial predictor-corrector interior-point algorithm for convex quadratic programming based on a modified predictor-corrector interior-point algorithm. In this algorithm, there is only one c...This article presents a polynomial predictor-corrector interior-point algorithm for convex quadratic programming based on a modified predictor-corrector interior-point algorithm. In this algorithm, there is only one corrector step after each predictor step, where Step 2 is a predictor step and Step 4 is a corrector step in the algorithm. In the algorithm, the predictor step decreases the dual gap as much as possible in a wider neighborhood of the central path and the corrector step draws iteration points back to a narrower neighborhood and make a reduction for the dual gap. It is shown that the algorithm has O（√nL） iteration complexity which is the best result for convex quadratic programming so far.展开更多
In this paper, we propose an arc-search interior-point algorithm for convex quadratic programming with a wide neighborhood of the central path, which searches the optimizers along the ellipses that approximate the ent...In this paper, we propose an arc-search interior-point algorithm for convex quadratic programming with a wide neighborhood of the central path, which searches the optimizers along the ellipses that approximate the entire central path. The favorable polynomial complexity bound of the algorithm is obtained, namely O（nlog（（ x^0）~TS^0/ε）） which is as good as the linear programming analogue. Finally, the numerical experiments show that the proposed algorithm is efficient.展开更多
In this paper, on the basis of the logarithmic barrier function and KKT conditions, we propose a combined homotopy infeasible interior-point method （CHIIP） for convex nonlinear programming problems. For any convex n...In this paper, on the basis of the logarithmic barrier function and KKT conditions, we propose a combined homotopy infeasible interior-point method （CHIIP） for convex nonlinear programming problems. For any convex nonlinear programming, without strict convexity for the logarithmic barrier function, we get different solutions of the convex programming in different cases by CHIIP method.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
For a multiobjective bilevel programnfing problem （P） with an extremal-value function, its dual problem is constructed by using the Fenchel-Moreau conjugate of the functions involved. Under some convexity and monoto...For a multiobjective bilevel programnfing problem （P） with an extremal-value function, its dual problem is constructed by using the Fenchel-Moreau conjugate of the functions involved. Under some convexity and monotonicity assumptions, the weak and strong duality assertions are obtained.展开更多
Two new versions of accelerated first-order methods for minimizing convex composite functions are proposed. In this paper, we first present an accelerated first-order method which chooses the step size 1/ Lk to be 1/ ...Two new versions of accelerated first-order methods for minimizing convex composite functions are proposed. In this paper, we first present an accelerated first-order method which chooses the step size 1/ Lk to be 1/ L0 at the beginning of each iteration and preserves the computational simplicity of the fast iterative shrinkage-thresholding algorithm. The first proposed algorithm is a non-monotone algorithm. To avoid this behavior, we present another accelerated monotone first-order method. The proposed two accelerated first-order methods are proved to have a better convergence rate for minimizing convex composite functions. Numerical results demonstrate the efficiency of the proposed two accelerated first-order methods.展开更多
基金supported by the National Natural Science Foundation of China(No.62203256)。
文摘Generating dynamically feasible trajectory for fixed-wing Unmanned Aerial Vehicles(UAVs)in dense obstacle environments remains computationally intractable.This paper proposes a Safe Flight Corridor constrained Sequential Convex Programming(SFC-SCP)to improve the computation efficiency and reliability of trajectory generation.SFC-SCP combines the front-end convex polyhedron SFC construction and back-end SCP-based trajectory optimization.A Sparse A^(*)Search(SAS)driven SFC construction method is designed to efficiently generate polyhedron SFC according to the geometric relation among obstacles and collision-free waypoints.Via transforming the nonconvex obstacle-avoidance constraints to linear inequality constraints,SFC can mitigate infeasibility of trajectory planning and reduce computation complexity.Then,SCP casts the nonlinear trajectory optimization subject to SFC into convex programming subproblems to decrease the problem complexity.In addition,a convex optimizer based on interior point method is customized,where the search direction is calculated via successive elimination to further improve efficiency.Simulation experiments on dense obstacle scenarios show that SFC-SCP can generate dynamically feasible safe trajectory rapidly.Comparative studies with state-of-the-art SCP-based methods demonstrate the efficiency and reliability merits of SFC-SCP.Besides,the customized convex optimizer outperforms off-the-shelf optimizers in terms of computation time.
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.
基金National Basic Research Program of China(2011CB707000)Innovative Research Group National Natural Science Foundation of China(60921001)
文摘The detection of sparse signals against background noise is considered. Detecting signals of such kind is difficult since only a small portion of the signal carries information. Prior knowledge is usually assumed to ease detection. In this paper, we consider the general unknown and arbitrary sparse signal detection problem when no prior knowledge is available. Under a Ney- man-Pearson hypothesis-testing framework, a new detection scheme is proposed by combining a generalized likelihood ratio test （GLRT）-Iike test statistic and convex programming methods which directly exploit sparsity in an underdetermined system of linear equations. We characterize large sample behavior of the proposed method by analyzing its asymptotic performance. Specifically, we give the condition for the Chernoff-consistent detection which shows that the proposed method is very sensitive to the norm energy of the sparse signals. Both the false alam rate and the miss rate tend to zero at vanishing signal-to-noise ratio （SNR）, as long as the signal energy grows at least logarithmically with the problem dimension. Next we give a large deviation analysis to characterize the error exponent for the Neyman-Pearson detection. We derive the oracle error exponent assuming signal knowledge. Then we explicitly derive the error exponent of the proposed scheme and compare it with the oracle exponent. We complement our study with numerical experiments, showing that the proposed method performs in the vicinity of the likelihood ratio test （LRT） method in the finite sample scenario and the error probability degrades exponentially with the number of observations.
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A potential reduction algorithm is proposed for optimization of a convex function subject to linear constraints.At each step of the algorithm,a system of linear equations is solved to get a search direction and the Armijo's rule is used to determine a stepsize.It is proved that the algorithm is globally convergent.Computational results are reported.
文摘An algorithm for solving a class of smooth convex programming is given. Using smooth exact multiplier penalty function, a smooth convex programming is minimized to a minimizing strongly convex function on the compact set was reduced. Then the strongly convex function with a Newton method on the given compact set was minimized.
基金Projcct Supported by National Natural Science Foundation of,China
文摘In this paper,we present two parallel multiplicative algorithms for convex programming.If the objective function has compact level sets and has a locally Lipschitz continuous gradient,we discuss convergence of the algorithms.The proofs are essentially based on the results of sequential methods shown by Eggermontt[1].
文摘In this paper, we establish the second-order differential equation system with the feedback controls for solving the problem of convex programming. Using Lagrange function and projection operator, the equivalent operator equations for the convex programming problems under the certain conditions are obtained. Then a second-order differential equation system with the feedback controls is constructed on the basis of operator equation. We prove that any accumulation point of the trajectory of the second-order differential equation system with the feedback controls is a solution to the convex programming problem. In the end, two examples using this differential equation system are solved. The numerical results are reported to verify the effectiveness of the second-order differential equation system with the feedback controls for solving the convex programming problem.
基金supported by the National Natural Science Foundation of China(Grant No.12372044).
文摘With the rapid changes of the flight environment and situation,there will be various unexpected situations while multiple missiles are performing the missions.To fast cope with the various situations in mission executions,the conventional sequential convex programming algorithm and the parallel-based sequential convex programming algorithm for multiple missiles fast trajectory replanning are proposed in this paper.The originally non-convex trajectory optimization problem is reformulated into a series of convex optimization subproblems based on the sequential convex programming method.The conventional sequential convex programming algorithm is developed through linearization,successive convexification,and relaxation techniques to solve the convex optimization subproblems iteratively.However,multiple missiles are related through various cooperative constraints.When the trajectory optimization of multiple missiles is formulated as an optimal control problem to solve,the complexity of the problem will increase dramatically as the number of missiles increases.To alleviate the coupled effect caused by multiple aerodynamically controlled missiles,the parallel-based sequential convex programming algorithm is proposed to solve the trajectory optimization problem for multiple missiles in parallel,reducing the complexity of the trajectory optimization problem and significantly shortening the computation time.Numerical simulations are provided to verify the convergence and effectiveness of the conventional sequential convex programming algorithm and the parallel-based sequential convex programming algorithm to cope with the trajectory optimization problem with various constraints.Furthermore,the optimality and the real-time performance of the proposed algorithms are discussed in comparative simulation examples.
基金National Natural Science Foundation of China(10261001)Science Foundation of Guangxi(0236001)
文摘A class of functions and a sort of nonlinear programming called respectively E-convex functions and E-convex programming were presented and studied recently by Youness in [1], In this paper, we point out the most results for .E-convex functions and E-convex programming in [1] are not true by six counter examples.
基金This work was mainly done while the first author was visiting the University of Bayreuth, and was supported by the Chinese Scholarship Council, German Academic Exchange Service （DAAD） and the National Natural Science Foundation of China.
文摘In this paper, we describe a method to solve large-scale structural optimization problems by sequential convex programming （SCP）. A predictor-corrector interior point method is applied to solve the strictly convex subproblems. The SCP algorithm and the topology optimization approach are introduced. Especially, different strategies to solve certain linear systems of equations are analyzed. Numerical results are presented to show the efficiency of the proposed method for solving topology optimization problems and to compare different variants.
基金Acknowledgements This work was supported by the National Natural Science Foundation of China （Grant Nos. 11671116, 11271107, 91630202） and the Natural Science Foundation of Hebei Province of China （No. A2015202365）.
文摘The strictly contractive Peaceman-Rachford splitting method is one of effective methods for solving separable convex optimization problem, and the inertial proximal Peaceman-Rachford splitting method is one of its important variants. It is known that the convergence of the inertial proximal Peaceman- Rachford splitting method can be ensured if the relaxation factor in Lagrangian multiplier updates is underdetermined, which means that the steps for the Lagrangian multiplier updates are shrunk conservatively. Although small steps play an important role in ensuring convergence, they should be strongly avoided in practice. In this article, we propose a relaxed inertial proximal Peaceman- Rachford splitting method, which has a larger feasible set for the relaxation factor. Thus, our method provides the possibility to admit larger steps in the Lagrangian multiplier updates. We establish the global convergence of the proposed algorithm under the same conditions as the inertial proximal Peaceman-Rachford splitting method. Numerical experimental results on a sparse signal recovery problem in compressive sensing and a total variation based image denoising problem demonstrate the effectiveness of our method.
文摘This paper gives a new dual problem for nondifferentiable convex programming and provesthe properties of weak duality and strong duality and offers a necessary and sufficient condition ofstrong duality.
基金Bing-Sheng He and Ming-Hua Xu were supported by the National Natural Science Foundation of China(No.11471156)Xiao-Ming Yuan was supported by the General Research Fund from Hong Kong Research Grants Council(No.HKBU 12313516).
文摘It has been shown that the alternating direction method of multipliers(ADMM)is not necessarily convergent when it is directly extended to a multiple-block linearly constrained convex minimization model with an objective function that is in the sum of more than two functions without coupled variables.Recently,we pro-posed the block-wise ADMM,which was obtained by regrouping the variables and functions of such a model as two blocks and then applying the original ADMM in block-wise.This note is a further study on this topic with the purpose of showing that a well-known relaxation factor proposed by Fortin and Glowinski for iteratively updat-ing the Lagrangian multiplier of the originalADMMcan also be used in the block-wise ADMM.We thus propose the block-wise ADMM with Fortin and Glowinski’s relax-ation factor for the multiple-block convex minimization model.Like the block-wise ADMM,we also suggest further decomposing the resulting subproblems and regular-izing them by proximal terms to ensure the convergence.For the block-wise ADMM with Fortin and Glowinski's relaxation factor,its convergence and worst-case conver-gence rate measured by the iteration complexity in the ergodic sense are derived.
基金Project supported by the National Science Foundation of China (60574071) the Foundation for University Key Teacher by the Ministry of Education.
文摘This article presents a polynomial predictor-corrector interior-point algorithm for convex quadratic programming based on a modified predictor-corrector interior-point algorithm. In this algorithm, there is only one corrector step after each predictor step, where Step 2 is a predictor step and Step 4 is a corrector step in the algorithm. In the algorithm, the predictor step decreases the dual gap as much as possible in a wider neighborhood of the central path and the corrector step draws iteration points back to a narrower neighborhood and make a reduction for the dual gap. It is shown that the algorithm has O（√nL） iteration complexity which is the best result for convex quadratic programming so far.
基金Supported by the National Natural Science Foundation of China(71471102)
文摘In this paper, we propose an arc-search interior-point algorithm for convex quadratic programming with a wide neighborhood of the central path, which searches the optimizers along the ellipses that approximate the entire central path. The favorable polynomial complexity bound of the algorithm is obtained, namely O（nlog（（ x^0）~TS^0/ε）） which is as good as the linear programming analogue. Finally, the numerical experiments show that the proposed algorithm is efficient.
文摘In this paper, on the basis of the logarithmic barrier function and KKT conditions, we propose a combined homotopy infeasible interior-point method （CHIIP） for convex nonlinear programming problems. For any convex nonlinear programming, without strict convexity for the logarithmic barrier function, we get different solutions of the convex programming in different cases by CHIIP method.
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(Grant No.11171250)
文摘For a multiobjective bilevel programnfing problem （P） with an extremal-value function, its dual problem is constructed by using the Fenchel-Moreau conjugate of the functions involved. Under some convexity and monotonicity assumptions, the weak and strong duality assertions are obtained.
基金Sponsored by the National Natural Science Foundation of China(Grant No.11461021)the Natural Science Basic Research Plan in Shaanxi Province of China(Grant No.2017JM1014)
文摘Two new versions of accelerated first-order methods for minimizing convex composite functions are proposed. In this paper, we first present an accelerated first-order method which chooses the step size 1/ Lk to be 1/ L0 at the beginning of each iteration and preserves the computational simplicity of the fast iterative shrinkage-thresholding algorithm. The first proposed algorithm is a non-monotone algorithm. To avoid this behavior, we present another accelerated monotone first-order method. The proposed two accelerated first-order methods are proved to have a better convergence rate for minimizing convex composite functions. Numerical results demonstrate the efficiency of the proposed two accelerated first-order methods.
