Xu Chengxian

A new two-level linear relaxed bound method for geometric programming problems

In this paper a new two-level linear relaxed bound method is proposed for solving the global solution of geometric programming problems, and its convergent properties is proved, and a numerical example is used to illustrate the effectiveness of the presented algorithm. The bound technique in this algorithm is different from the other ones. The two-level relaxed linear programming problems of geometric programming problems are given without additional new variables and constraints by making use of the linear approximation of power functions and the new formulas for product to be unequal with sum. 2004 Elsevier Inc. All rights reserved.

Adaptive nonlinear control with partial overparametrization

Abstract The main purpose of this paper is to show that overparametrization in adaptive nonlinear control is not always a bad thing and can be intentionally introduced to achieve similar performance with less control effort. To this end, an adaptive controller with partial overparametrization is first designed to solve the regulation problem of parametric-strict-feedback form nonlinear systems by combining the design procedure in Krstic et al. (System Control Lett. 19 (1992) 177) with that in Kanellakopoulos et al. (IEEE Trans. Automat. Control 36 (1991) 1241). Then, to reduce the control effort needed by the above controller further, a modified adaptive controller is designed by introducing a reference signal and reformulating the regulation problem as a tracking problem. The simulation results show that, compared with the adaptive controller without overparametrization, the adaptive controller with partial overparametrization can achieve similar performance with less control effort, and the modified one can do the same thing with even less control effort.

A Trust Regional Algorithm for Bound Constrained Minimization

A trust region algorithm is proposed for box constrained nonlinear optimization. At each step of the algorithm a quadratic model problem in a box is minimized. Global convergence and quadratic convergence rate to a strong local minimizer are given. Computational results are presented to show the efficiency of the algorithm

Stable factorized quasi-Newton methods for nonlinear least-squares problems

In this paper, we consider stable factorized quasi-Newton methods for solving nonlinear least-squares problems. Based on the QR decomposition of the Jacobian of the residual function, updating a rectangular correction matrix to the Jacobian is changed to updating a square matrix of lower order. A new class of factorized quasi-Newton methods is proposed. It is proved that this type of methods possesses locally superlinear convergence property under mild conditions. Numerical results compared with the original algorithms are presented.

Sequential quadratic programming methods for optimal control problems with state constraints

A kind of direct methods is presented for the solution of optimal control problems with state constraints. These methods are sequential quadratic programming methods. At every iteration a quadratic programming which is obtained by quadratic approximation to Lagrangian function and linear approximations to constraints is solved to get a search direction for a merit function. The merit function is formulated by augmenting the Lagrangian function with a penalty term. A line search is carried out along the search direction to determine a step length such that the merit function is decreased. The methods presented in this paper include continuous sequential quadratic programming methods and discreate sequential quadratic programming methods.

H-matrices and S-doubly diagonally dominant matrices

In this paper, the concept of the s-doubly diagonally dominant matrices is introduced and the properties of these matrices are discussed. With the properties of the s-doubly diagonally dominant matrices and the properties of comparison matrices, some equivalent conditions for H-matrices are presented. These conditions generalize and improve existing results about the equivalent conditions for H-matrices. Applications and examples using these new equivalent conditions are also presented, and a new inclusion region of k-multiple eigenvalues of matrices is obtained.

A minimizing algorithm for complex nonconvex nondifferentiable functions

The minimization of nonconvex, nondifferentiable functions that are compositions of max-type functions formed by nondifferentiable convex functions is discussed in this paper. It is closely related to practical engineering problems. By utilizing the globality of ε-subdifferential and the theory of quasidifferential, and by introducing a new scheme which selects several search directions and consider them simultaneously at each iteration, a minimizing algorithm is derived. It is simple in structure, implementable, numerically efficient and has global convergence. The shortcomings of the existing algorithms are thus overcome both in theory and in application.