By introducing a smooth merit function for the median function, a new smooth merit function for box constrained variational inequalities （BVIs） was constructed. The function is simple and has some good differential ...By introducing a smooth merit function for the median function, a new smooth merit function for box constrained variational inequalities （BVIs） was constructed. The function is simple and has some good differential properties. A damped Newton type method was presented based on it. Global and local superlinear/ quadratic convergence results were obtained under mild conditions, and the finite termination property was also shown for the linear BVIs. Numerical results suggest that the method is efficient and promising.展开更多
The authors consider optimization methods for box constrained variational inequalities. First, the authors study the KKT-conditions problem based on the original problem. A merit function for the KKT-conditions proble...The authors consider optimization methods for box constrained variational inequalities. First, the authors study the KKT-conditions problem based on the original problem. A merit function for the KKT-conditions problem is proposed, and some desirable properties of the merit function are obtained. Through the merit function, the original problem is reformulated as minimization with simple constraints. Then, the authors show that any stationary point of the optimization problem is a solution of the original problem. Finally, a descent algorithm is presented for the optimization problem, and global convergence is shown.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
We establish in this paper optimal parametric Lagrangian dual models for box constrained quadratic program based on the generalized D.C.(difference between convex) optimization approach,which can be reformulated as se...We establish in this paper optimal parametric Lagrangian dual models for box constrained quadratic program based on the generalized D.C.(difference between convex) optimization approach,which can be reformulated as semidefinite programming problems.As an application,we propose new valid linear constraints for rank-one relaxation.展开更多
In this paper, we first give a smoothing approximation function of nonsmooth system based on box constrained variational inequalities and then present a new smoothing approximation algorithm. Under suitable conditions...In this paper, we first give a smoothing approximation function of nonsmooth system based on box constrained variational inequalities and then present a new smoothing approximation algorithm. Under suitable conditions,we show that the method is globally and superlinearly convergent. A few numerical results are also reported in the paper.展开更多
This paper proposes a novel hypersphere support vector machines （HSVMs） based on generalized multiplicative updates. This algorithm can obtain the boundary of hypersphere containing one class of samples by the descr...This paper proposes a novel hypersphere support vector machines （HSVMs） based on generalized multiplicative updates. This algorithm can obtain the boundary of hypersphere containing one class of samples by the description of the training samples from one class and use this boundary to classify the test samples. The generalized multiplicative updates are applied to solving boundary optimization progranmning. Multiplicative updates available are suited for nonnegative quadratic convex programming. The generalized multiplicative updates are derived to box and sum constrained quadratic programming in this paper. They provide an extremely straightforward way to implement support vector machines （SVMs） where all variables are updated in parallel. The generalized multiplicative updates converge monotonically to the solution of the maximum margin hyperplane. The experiments show the superiority of our new algorithm.展开更多
This paper proposes an arlene scaling derivative-free trust region method with interior backtracking technique for bounded-constrained nonlinear programming. This method is designed to get a stationary point for such ...This paper proposes an arlene scaling derivative-free trust region method with interior backtracking technique for bounded-constrained nonlinear programming. This method is designed to get a stationary point for such a problem with polynomial interpolation models instead of the objective function in trust region subproblem. Combined with both trust region strategy and line search technique, at each iteration, the affine scaling derivative-free trust region subproblem generates a backtracking direction in order to obtain a new accepted interior feasible step. Global convergence and fast local convergence properties are established under some reasonable conditions. Some numerical results are also given to show the effectiveness of the proposed algorithm.展开更多
文摘By introducing a smooth merit function for the median function, a new smooth merit function for box constrained variational inequalities （BVIs） was constructed. The function is simple and has some good differential properties. A damped Newton type method was presented based on it. Global and local superlinear/ quadratic convergence results were obtained under mild conditions, and the finite termination property was also shown for the linear BVIs. Numerical results suggest that the method is efficient and promising.
基金the National Natural Science Foundation of China(No.19971002)
文摘The authors consider optimization methods for box constrained variational inequalities. First, the authors study the KKT-conditions problem based on the original problem. A merit function for the KKT-conditions problem is proposed, and some desirable properties of the merit function are obtained. Through the merit function, the original problem is reformulated as minimization with simple constraints. Then, the authors show that any stationary point of the optimization problem is a solution of the original problem. Finally, a descent algorithm is presented for the optimization problem, and global convergence is shown.
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.
基金supported by National Natural Science Foundation of China(Grant Nos. 11001006 and 91130019/A011702)the Fund of State Key Laboratory of Software Development Environment (Grant No. SKLSDE-2011ZX-15.)
文摘We establish in this paper optimal parametric Lagrangian dual models for box constrained quadratic program based on the generalized D.C.(difference between convex) optimization approach,which can be reformulated as semidefinite programming problems.As an application,we propose new valid linear constraints for rank-one relaxation.
文摘In this paper, we first give a smoothing approximation function of nonsmooth system based on box constrained variational inequalities and then present a new smoothing approximation algorithm. Under suitable conditions,we show that the method is globally and superlinearly convergent. A few numerical results are also reported in the paper.
基金Project supported by the National Natural Science Foundation of China (Grant No.60574075)
文摘This paper proposes a novel hypersphere support vector machines （HSVMs） based on generalized multiplicative updates. This algorithm can obtain the boundary of hypersphere containing one class of samples by the description of the training samples from one class and use this boundary to classify the test samples. The generalized multiplicative updates are applied to solving boundary optimization progranmning. Multiplicative updates available are suited for nonnegative quadratic convex programming. The generalized multiplicative updates are derived to box and sum constrained quadratic programming in this paper. They provide an extremely straightforward way to implement support vector machines （SVMs） where all variables are updated in parallel. The generalized multiplicative updates converge monotonically to the solution of the maximum margin hyperplane. The experiments show the superiority of our new algorithm.
基金supported by the National Science Foundation of China under Grant No.11371253
文摘This paper proposes an arlene scaling derivative-free trust region method with interior backtracking technique for bounded-constrained nonlinear programming. This method is designed to get a stationary point for such a problem with polynomial interpolation models instead of the objective function in trust region subproblem. Combined with both trust region strategy and line search technique, at each iteration, the affine scaling derivative-free trust region subproblem generates a backtracking direction in order to obtain a new accepted interior feasible step. Global convergence and fast local convergence properties are established under some reasonable conditions. Some numerical results are also given to show the effectiveness of the proposed algorithm.
