PolyU IR Community:
http://hdl.handle.net/10397/10
2015-01-27T09:36:46ZStabilization of wave systems with input delay in the boundary control
http://hdl.handle.net/10397/7029
Title: Stabilization of wave systems with input delay in the boundary control
Authors: Xu, Gen Qi; Yung, Siu Pang; Li, Leong-kwan
Abstract: In the present paper, we consider a wave system that is fixed at one end and a boundary control input possessing a partial time delay of weight (1 - μ) is applied over the other end. Using a simple boundary velocity feedback law, we show that the closed loop system generates a C₀ group of linear operators. After a spectral analysis, we show that the closed loop system is a Riesz one, that is, there is a sequence of eigenvectors and generalized eigenvectors that forms a Riesz basis for the state Hubert space. Furthermore, we show that when the weight μ > 1/2, for any time delay, we can choose a suitable feedback gain so that the closed loop system is exponentially stable. When μ = 1/2 we show that the system is at most asymptotically stable. When μ < 1/2, the system is always unstable.2006-10-01T00:00:00ZOptimality conditions for nonsmooth generalized semi-infinite programs
http://hdl.handle.net/10397/7021
Title: Optimality conditions for nonsmooth generalized semi-infinite programs
Authors: Chen, Zhangyou; Chen, Zhe
Abstract: We consider a class of nonsmooth generalized semi-infinite programming problems. We apply results from parametric optimization to the lower level problems of generalized semi-infinite programming problems to get estimates for the value functions of the lower level problems and thus derive necessary optimality conditions for generalized semi-infinite programming problems. We also derive some new estimates for the value functions of the lower level problems in terms of generalized differentiation and further obtain the necessary optimality conditions.2013-01-01T00:00:00ZWorst-case complexity of smoothing quadratic regularization methods for non-lipschitzian optimization
http://hdl.handle.net/10397/7015
Title: Worst-case complexity of smoothing quadratic regularization methods for non-lipschitzian optimization
Authors: Bian, Wei; Chen, Xiaojun
Abstract: In this paper, we propose a smoothing quadratic regularization (SQR) algorithm for solving a class of nonsmooth nonconvex, perhaps even non-Lipschitzian minimization problems, which has wide applications in statistics and sparse reconstruction. The proposed SQR algorithm is a first order method. At each iteration, the SQR algorithm solves a strongly convex quadratic minimization problem with a diagonal Hessian matrix, which has a simple closed-form solution that is inexpensive to calculate. We show that the worst-case complexity of reaching an ϵ scaled stationary point is $O(ϵ⁻²). Moreover, if the objective function is locally Lipschitz continuous, the SQR algorithm with a slightly modified updating scheme for the smoothing parameter and iterate can obtain an ϵ Clarke stationary point in at most $O(ϵ⁻³) iterations.2013-01-01T00:00:00ZOptimality conditions and a smoothing trust region newton method for nonlipschitz optimization
http://hdl.handle.net/10397/7014
Title: Optimality conditions and a smoothing trust region newton method for nonlipschitz optimization
Authors: Chen, Xiaojun; Niu, Lingfeng; Yuan, Yaxiang
Abstract: Regularized minimization problems with nonconvex, nonsmooth, perhaps non-Lipschitz penalty functions have attracted considerable attention in recent years, owing to their wide applications in image restoration, signal reconstruction, and variable selection. In this paper, we derive affine-scaled second order necessary and sufficient conditions for local minimizers of such minimization problems. Moreover, we propose a global convergent smoothing trust region Newton method which can find a point satisfying the affine-scaled second order necessary optimality condition from any starting point. Numerical examples are given to demonstrate the effectiveness of the smoothing trust region Newton method.2013-01-01T00:00:00Z