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
Hanson and Mond have grven sets of necessary and sufficient conditions for optimality in constrained optimization by introducing classes of generalized functions, called type Ⅰ functions. Recently, Bector definded un...Hanson and Mond have grven sets of necessary and sufficient conditions for optimality in constrained optimization by introducing classes of generalized functions, called type Ⅰ functions. Recently, Bector definded univex functions, a new class of functions that unifies several concepts of generalized convexity. In this paper, additional conditions are attached to the Kuhn Tucker conditions giving a set of conditions which are both necessary and sufficient for optimality in constrained optimization, under appropriate constraint qualifications.展开更多
An improved approach is presented in this paper to implement highly constrained cooperative guidance to attack a stationary target.The problem with time-varying Proportional Navigation(PN)gain is first formulated as a...An improved approach is presented in this paper to implement highly constrained cooperative guidance to attack a stationary target.The problem with time-varying Proportional Navigation(PN)gain is first formulated as a nonlinear optimal control problem,which is difficult to solve due to the existence of nonlinear kinematics and nonconvex constraints.After convexification treatments and discretization,the solution to the original problem can be approximately obtained by solving a sequence of Second-Order Cone Programming(SOCP)problems,which can be readily solved by state-of-the-art Interior-Point Methods(IPMs).To mitigate the sensibility of the algorithm on the user-provided initial profile,a Two-Stage Sequential Convex Programming(TSSCP)method is presented in detail.Furthermore,numerical simulations under different mission scenarios are conducted to show the superiority of the proposed method in solving the cooperative guidance problem.The research indicated that the TSSCP method is more tractable and reliable than the traditional methods and has great potential for real-time processing and on-board implementation.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
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
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
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
This paper presents a new heuristic to linearise the convex quadratic programming problem. The usual Karush-Kuhn-Tucker conditions are used but in this case a linear objective function is also formulated from the set ...This paper presents a new heuristic to linearise the convex quadratic programming problem. The usual Karush-Kuhn-Tucker conditions are used but in this case a linear objective function is also formulated from the set of linear equations and complementarity slackness conditions. An unboundedness challenge arises in the proposed formulation and this challenge is alleviated by construction of an additional constraint. The formulated linear programming problem can be solved efficiently by the available simplex or interior point algorithms. There is no restricted base entry in this new formulation. Some computational experiments were carried out and results are provided.展开更多
In the past few years, much and much attention has been paid to the method for solving non-convex programming. Many convergence results are obtained for bounded sets. In this paper, we get global convergence results f...In the past few years, much and much attention has been paid to the method for solving non-convex programming. Many convergence results are obtained for bounded sets. In this paper, we get global convergence results for non-convex programming in unbounded sets under suitable conditions.展开更多
For satate form linear gram as Fang and sao deined and approach which would find an optimal solution by solving an anconstrained convex dual programming.Thedual was construcied by applying an emropic peturbation and a...For satate form linear gram as Fang and sao deined and approach which would find an optimal solution by solving an anconstrained convex dual programming.Thedual was construcied by applying an emropic peturbation and a simple Inequality Inz【z-1 for z】0n,In this paper,we suggest than a paperbation functiontake the place of Inx such that the new approdt has good numerical stability andhas all properties of the original展开更多
The simplified Newton method, at the expense of fast convergence, reduces the work required by Newton method by reusing the initial Jacobian matrix. The composite Newton method attempts to balance the trade-off betwee...The simplified Newton method, at the expense of fast convergence, reduces the work required by Newton method by reusing the initial Jacobian matrix. The composite Newton method attempts to balance the trade-off between expense and fast convergence by composing one Newton step with one simplified Newton step. Recently, Mehrotra suggested a predictor-corrector variant of primal-dual interior point method for linear programming. It is currently the interiorpoint method of the choice for linear programming. In this work we propose a predictor-corrector interior-point algorithm for convex quadratic programming. It is proved that the algorithm is equivalent to a level-1 perturbed composite Newton method. Computations in the algorithm do not require that the initial primal and dual points be feasible. Numerical experiments are made.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
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
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
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
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
The definition of generalized unified (C, α, ρ, d)-convex function is given. The concepts of generalized unified (C, α, ρ, d)-quasiconvexity, generalized unified (C, α, ρ, d)-pseudoconvexity and generalized unif...The definition of generalized unified (C, α, ρ, d)-convex function is given. The concepts of generalized unified (C, α, ρ, d)-quasiconvexity, generalized unified (C, α, ρ, d)-pseudoconvexity and generalized unified (C, α, ρ, d)-strictly pseudoconvex functions are presented. The sufficient optimality conditions for multiobjective nonsmooth semi-infinite programming are obtained involving these generalized convexity lastly.展开更多
The definitions of generalized pseudoconvex,generalized quasiconvex and its stri ctly generalized convexity were presented for the static programming at locally star -shaped set using the concept of right-upper deriva...The definitions of generalized pseudoconvex,generalized quasiconvex and its stri ctly generalized convexity were presented for the static programming at locally star -shaped set using the concept of right-upper derivative and the concept of sub linear. The sufficient and necessary conditions of the static programming were d erived in terms of a generalized Lemma in this paper. The results obtained are u seful for the further study on the duality of static programming and cover many already known conditions.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
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Hanson and Mond have grven sets of necessary and sufficient conditions for optimality in constrained optimization by introducing classes of generalized functions, called type Ⅰ functions. Recently, Bector definded univex functions, a new class of functions that unifies several concepts of generalized convexity. In this paper, additional conditions are attached to the Kuhn Tucker conditions giving a set of conditions which are both necessary and sufficient for optimality in constrained optimization, under appropriate constraint qualifications.
基金supported by the Joint Foundation of the Ministry of Education of China(No.6141A02022340).
文摘An improved approach is presented in this paper to implement highly constrained cooperative guidance to attack a stationary target.The problem with time-varying Proportional Navigation(PN)gain is first formulated as a nonlinear optimal control problem,which is difficult to solve due to the existence of nonlinear kinematics and nonconvex constraints.After convexification treatments and discretization,the solution to the original problem can be approximately obtained by solving a sequence of Second-Order Cone Programming(SOCP)problems,which can be readily solved by state-of-the-art Interior-Point Methods(IPMs).To mitigate the sensibility of the algorithm on the user-provided initial profile,a Two-Stage Sequential Convex Programming(TSSCP)method is presented in detail.Furthermore,numerical simulations under different mission scenarios are conducted to show the superiority of the proposed method in solving the cooperative guidance problem.The research indicated that the TSSCP method is more tractable and reliable than the traditional methods and has great potential for real-time processing and on-board implementation.
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.
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.
文摘This paper presents a new heuristic to linearise the convex quadratic programming problem. The usual Karush-Kuhn-Tucker conditions are used but in this case a linear objective function is also formulated from the set of linear equations and complementarity slackness conditions. An unboundedness challenge arises in the proposed formulation and this challenge is alleviated by construction of an additional constraint. The formulated linear programming problem can be solved efficiently by the available simplex or interior point algorithms. There is no restricted base entry in this new formulation. Some computational experiments were carried out and results are provided.
基金The NNSF (10071031) of China China Postdoctoral Science Foundation.
文摘In the past few years, much and much attention has been paid to the method for solving non-convex programming. Many convergence results are obtained for bounded sets. In this paper, we get global convergence results for non-convex programming in unbounded sets under suitable conditions.
基金The project was supported by the National Natural Science Fundation of China
文摘For satate form linear gram as Fang and sao deined and approach which would find an optimal solution by solving an anconstrained convex dual programming.Thedual was construcied by applying an emropic peturbation and a simple Inequality Inz【z-1 for z】0n,In this paper,we suggest than a paperbation functiontake the place of Inx such that the new approdt has good numerical stability andhas all properties of the original
文摘The simplified Newton method, at the expense of fast convergence, reduces the work required by Newton method by reusing the initial Jacobian matrix. The composite Newton method attempts to balance the trade-off between expense and fast convergence by composing one Newton step with one simplified Newton step. Recently, Mehrotra suggested a predictor-corrector variant of primal-dual interior point method for linear programming. It is currently the interiorpoint method of the choice for linear programming. In this work we propose a predictor-corrector interior-point algorithm for convex quadratic programming. It is proved that the algorithm is equivalent to a level-1 perturbed composite Newton method. Computations in the algorithm do not require that the initial primal and dual points be feasible. Numerical experiments are made.
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.
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.
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.
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.
基金Supported by the Science Foundation of Shaanxi Provincial Educational Department Natural Science Foundation of China（06JK152） Supported by the Graduate Innovation Project of Yanan uni- versity（YCX201003）
文摘The definition of generalized unified (C, α, ρ, d)-convex function is given. The concepts of generalized unified (C, α, ρ, d)-quasiconvexity, generalized unified (C, α, ρ, d)-pseudoconvexity and generalized unified (C, α, ρ, d)-strictly pseudoconvex functions are presented. The sufficient optimality conditions for multiobjective nonsmooth semi-infinite programming are obtained involving these generalized convexity lastly.
基金National Natural Science Foundation ofChina(No.70273029)
文摘The definitions of generalized pseudoconvex,generalized quasiconvex and its stri ctly generalized convexity were presented for the static programming at locally star -shaped set using the concept of right-upper derivative and the concept of sub linear. The sufficient and necessary conditions of the static programming were d erived in terms of a generalized Lemma in this paper. The results obtained are u seful for the further study on the duality of static programming and cover many already known conditions.
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].
