Dear Editor,This letter addresses the formation control problem for constrained underactuated autonomous underwater vehicles (AUVs). The feasibility condition of the virtual control law is eliminated by introducing a ...Dear Editor,This letter addresses the formation control problem for constrained underactuated autonomous underwater vehicles (AUVs). The feasibility condition of the virtual control law is eliminated by introducing a nonlinear state dependence function (NSDF) that transforms the state of each AUV in the formation.展开更多
A class of discontinuous penalty functions was proposed to solve constrained minimization problems with the integral approach to global optimization, m-mean value and v-variance optimality conditions of a constrained ...A class of discontinuous penalty functions was proposed to solve constrained minimization problems with the integral approach to global optimization, m-mean value and v-variance optimality conditions of a constrained and penalized minimization problem were investigated. A nonsequential algorithm was proposed. Numerical examples were given to illustrate the effectiveness of the algorithm.展开更多
This paper introduces a new exact and smooth penalty function to tackle constrained min-max problems. By using this new penalty function and adding just one extra variable, a constrained rain-max problem is transforme...This paper introduces a new exact and smooth penalty function to tackle constrained min-max problems. By using this new penalty function and adding just one extra variable, a constrained rain-max problem is transformed into an unconstrained optimization one. It is proved that, under certain reasonable assumptions and when the penalty parameter is sufficiently large, the minimizer of this unconstrained optimization problem is equivalent to the minimizer of the original constrained one. Numerical results demonstrate that this penalty function method is an effective and promising approach for solving constrained finite min-max problems.展开更多
In this paper, a new augmented Lagrangian penalty function for constrained optimization problems is studied. The dual properties of the augmented Lagrangian objective penalty function for constrained optimization prob...In this paper, a new augmented Lagrangian penalty function for constrained optimization problems is studied. The dual properties of the augmented Lagrangian objective penalty function for constrained optimization problems are proved. Under some conditions, the saddle point of the augmented Lagrangian objective penalty function satisfies the first-order Karush-Kuhn-Tucker (KKT) condition. Especially, when the KKT condition holds for convex programming its saddle point exists. Based on the augmented Lagrangian objective penalty function, an algorithm is developed for finding a global solution to an inequality constrained optimization problem and its global convergence is also proved under some conditions.展开更多
An interval algorlthm for inequality coustrained discrete minimax problems is described, in which the constrained and objective functions are C1 functions. First, based on the penalty function methods, we trans form t...An interval algorlthm for inequality coustrained discrete minimax problems is described, in which the constrained and objective functions are C1 functions. First, based on the penalty function methods, we trans form this problem to unconstrained optimization. Second, the interval extensions of the penalty functions and the test rules of region deletion are discussed. At last, we design an interval algorithm with the bisection rule of Moore. The algorithm provides bounds on both the minimax value and the localization of the minimax points of the problem. Numerical results show that algorithm is reliable and efficiency.展开更多
A new smooth gap function for the box constrained variational inequality problem （VIP） is proposed based on an integral global optimality condition. The smooth gap function is simple and has some good differentiable...A new smooth gap function for the box constrained variational inequality problem （VIP） is proposed based on an integral global optimality condition. The smooth gap function is simple and has some good differentiable properties. The box constrained VIP can be reformulated as a differentiable optimization problem by the proposed smooth gap function. The conditions, under which any stationary point of the optimization problem is the solution to the box constrained VIP, are discussed. A simple frictional contact problem is analyzed to show the applications of the smooth gap function. Finally, the numerical experiments confirm the good theoretical properties of the method.展开更多
The problems of optimal control (OCPs) related to PDEs are a very active area of research. These problems deal with the processes of mechanical engineering, heat aeronautics, physics, hydro and gas dynamics, the physi...The problems of optimal control (OCPs) related to PDEs are a very active area of research. These problems deal with the processes of mechanical engineering, heat aeronautics, physics, hydro and gas dynamics, the physics of plasma and other real life problems. In this paper, we deal with a class of the constrained OCP for parabolic systems. It is converted to new unconstrained OCP by adding a penalty function to the cost functional. The existence solution of the considering system of parabolic optimal control problem (POCP) is introduced. In this way, the uniqueness theorem for the solving POCP is introduced. Therefore, a theorem for the sufficient differentiability conditions has been proved.展开更多
In this paper,a new objective penalty function approach is proposed for solving minimax programming problems with equality and inequality constraints.This new objective penalty function combines the objective penalty ...In this paper,a new objective penalty function approach is proposed for solving minimax programming problems with equality and inequality constraints.This new objective penalty function combines the objective penalty and constraint penalty.By the new objective penalty function,a constrained minimax problem is converted to minimizations of a sequence of continuously differentiable functions with a simple box constraint.One can thus apply any efficient gradient minimization methods to solve the minimizations with box constraint at each step of the sequence.Some relationships between the original constrained minimax problem and the corresponding minimization problems with box constraint are established.Based on these results,an algorithm for finding a global solution of the constrained minimax problems is proposed by integrating the particular structure of minimax problems and its global convergence is proved under some conditions.Furthermore,an algorithm is developed for finding a local solution of the constrained minimax problems,with its convergence proved under certain conditions.Preliminary results of numerical experiments with well-known test problems show that satisfactorilyapproximate solutions for some constrained minimax problems can be obtained.展开更多
基金supported by the National Natural Science Foundation of China(62073094)the Fundamental Research Funds for the Central Universities(3072024GH0404)
文摘Dear Editor,This letter addresses the formation control problem for constrained underactuated autonomous underwater vehicles (AUVs). The feasibility condition of the virtual control law is eliminated by introducing a nonlinear state dependence function (NSDF) that transforms the state of each AUV in the formation.
文摘A class of discontinuous penalty functions was proposed to solve constrained minimization problems with the integral approach to global optimization, m-mean value and v-variance optimality conditions of a constrained and penalized minimization problem were investigated. A nonsequential algorithm was proposed. Numerical examples were given to illustrate the effectiveness of the algorithm.
基金supported by the Grant of the Academy of Mathematics and System Science of Chinese Academy of Sciences-The Hong Kong Polytechnic University Joint Research Institute (AMSS-PolyU)the Research Grands Council Grant of The Hong Kong Polytechnic University (No. 5365/09E)
文摘This paper introduces a new exact and smooth penalty function to tackle constrained min-max problems. By using this new penalty function and adding just one extra variable, a constrained rain-max problem is transformed into an unconstrained optimization one. It is proved that, under certain reasonable assumptions and when the penalty parameter is sufficiently large, the minimizer of this unconstrained optimization problem is equivalent to the minimizer of the original constrained one. Numerical results demonstrate that this penalty function method is an effective and promising approach for solving constrained finite min-max problems.
文摘In this paper, a new augmented Lagrangian penalty function for constrained optimization problems is studied. The dual properties of the augmented Lagrangian objective penalty function for constrained optimization problems are proved. Under some conditions, the saddle point of the augmented Lagrangian objective penalty function satisfies the first-order Karush-Kuhn-Tucker (KKT) condition. Especially, when the KKT condition holds for convex programming its saddle point exists. Based on the augmented Lagrangian objective penalty function, an algorithm is developed for finding a global solution to an inequality constrained optimization problem and its global convergence is also proved under some conditions.
文摘An interval algorlthm for inequality coustrained discrete minimax problems is described, in which the constrained and objective functions are C1 functions. First, based on the penalty function methods, we trans form this problem to unconstrained optimization. Second, the interval extensions of the penalty functions and the test rules of region deletion are discussed. At last, we design an interval algorithm with the bisection rule of Moore. The algorithm provides bounds on both the minimax value and the localization of the minimax points of the problem. Numerical results show that algorithm is reliable and efficiency.
基金Project supported by the National Natural Science Foundation of China(Nos.10902077,11172209, and 10572031)
文摘A new smooth gap function for the box constrained variational inequality problem （VIP） is proposed based on an integral global optimality condition. The smooth gap function is simple and has some good differentiable properties. The box constrained VIP can be reformulated as a differentiable optimization problem by the proposed smooth gap function. The conditions, under which any stationary point of the optimization problem is the solution to the box constrained VIP, are discussed. A simple frictional contact problem is analyzed to show the applications of the smooth gap function. Finally, the numerical experiments confirm the good theoretical properties of the method.
文摘The problems of optimal control (OCPs) related to PDEs are a very active area of research. These problems deal with the processes of mechanical engineering, heat aeronautics, physics, hydro and gas dynamics, the physics of plasma and other real life problems. In this paper, we deal with a class of the constrained OCP for parabolic systems. It is converted to new unconstrained OCP by adding a penalty function to the cost functional. The existence solution of the considering system of parabolic optimal control problem (POCP) is introduced. In this way, the uniqueness theorem for the solving POCP is introduced. Therefore, a theorem for the sufficient differentiability conditions has been proved.
基金This research was supported by Natural Science Foundation of Chongqing(Nos.cstc2013jjB00001 and cstc2011jjA00010)by Chongqing Municipal Education Commission(No.KJ120616).
文摘In this paper,a new objective penalty function approach is proposed for solving minimax programming problems with equality and inequality constraints.This new objective penalty function combines the objective penalty and constraint penalty.By the new objective penalty function,a constrained minimax problem is converted to minimizations of a sequence of continuously differentiable functions with a simple box constraint.One can thus apply any efficient gradient minimization methods to solve the minimizations with box constraint at each step of the sequence.Some relationships between the original constrained minimax problem and the corresponding minimization problems with box constraint are established.Based on these results,an algorithm for finding a global solution of the constrained minimax problems is proposed by integrating the particular structure of minimax problems and its global convergence is proved under some conditions.Furthermore,an algorithm is developed for finding a local solution of the constrained minimax problems,with its convergence proved under certain conditions.Preliminary results of numerical experiments with well-known test problems show that satisfactorilyapproximate solutions for some constrained minimax problems can be obtained.
