A DC programming approach for sensor network localization with uncertainties in anchor positions
- Authors: Wu, Changzhi , Li, Chaojie , Long, Qiang
- Date: 2014
- Type: Text , Journal article
- Relation: Journal of Industrial and Management Optimization Vol. 10, no. 3 (2014), p. 817-826
- Full Text: false
- Reviewed:
- Description: The sensor network localization with uncertainties in anchor positions has been studied in this paper. We formulate this problem as a DC (difference of two convex functions) programming. Then, a DC programming based algorithm has been proposed to solve such a problem. Simulation results obtained by our proposed method are better performance than those obtained by existing ones.
Distributed proximal-gradient method for convex optimization with inequality constraints
- Authors: Li, Jueyou , Wu, Changzhi , Wu, Zhiyou , Long, Qiang , Wang, Xiangyu
- Date: 2014
- Type: Text , Journal article
- Relation: ANZIAM Journal Vol. 56, no. 2 (2014), p. 160-178
- Full Text: false
- Reviewed:
- Description: We consider a distributed optimization problem over a multi-agent network, in which the sum of several local convex objective functions is minimized subject to global convex inequality constraints. We first transform the constrained optimization problem to an unconstrained one, using the exact penalty function method. Our transformed problem has a smaller number of variables and a simpler structure than the existing distributed primal-dual subgradient methods for constrained distributed optimization problems. Using the special structure of this problem, we then propose a distributed proximal-gradient algorithm over a time-changing connectivity network, and establish a convergence rate depending on the number of iterations, the network topology and the number of agents. Although the transformed problem is nonsmooth by nature, our method can still achieve a convergence rate, O (1/k), after k iterations, which is faster than the rate, O (1/k), of existing distributed subgradient-based methods. Simulation experiments on a distributed state estimation problem illustrate the excellent performance of our proposed method. Copyright © 2014 Australian Mathematical Society.
A direct optimization method for low group delay FIR filter design
- Authors: Wu, Changzhi , Gao, David , Lay Teo, Kok
- Date: 2013
- Type: Text , Journal article
- Relation: Signal Processing Vol. 93, no. 7 (2013), p. 1764-1772
- Full Text: false
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- Description: This paper studies the design of FIR filter with low group delay, where the desired phase response is not being approximated. It is formulated as a constrained optimization problem, which is then solved globally. Numerical experiments show that our design method can produce a filter with smaller group delay than that obtained by the existing convex optimization method used in conjunction with a minimum phase spectral factorization method under the same design criteria. Furthermore, our formulation offers us the flexibility for the trade-off between the group delay and the magnitude response directly. It also allows the feasibility of imposing constraints on the group delay. © 2013 Elsevier B.V.
- Description: 2003011019
A quasisecant method for solving a system of nonsmooth equations
- Authors: Long, Qiang , Wu, Changzhi
- Date: 2013
- Type: Text , Journal article
- Relation: Computers and Mathematics with Applications Vol. 66, no. 4 (2013), p. 419-431
- Full Text: false
- Reviewed:
- Description: In this paper, the solution of nonsmooth equations is studied. We first transform the problem into an equivalent nonsmooth optimization problem and then the quasisecant method is introduced to solve it. Some nonsmooth equations that have arisen from bilevel programming problems are solved by our proposed method. The numerical results show the effectiveness and efficiency of our proposed method. © 2013 Elsevier Ltd. All rights reserved.
- Description: 2003011208
Min-max optimal control of linear systems with uncertainty and terminal state constraints
- Authors: Wu, Changzhi , Lay Teo, Kok , Wu, Soonyi
- Date: 2013
- Type: Text , Journal article
- Relation: Automatica Vol. 49, no. 6 (2013), p. 1809-1815
- Full Text: false
- Reviewed:
- Description: In this paper, a class of min-max optimal control problems with continuous dynamical systems and quadratic terminal constraints is studied. The main contribution is that the original terminal state constraint in which the disturbance is involved is transformed into an equivalent linear matrix inequality without disturbance under certain conditions. Then, the original min-max optimal control problem is solved via solving a sequence of semi-definite programming problems. An example is presented to illustrate the proposed method. © 2013 Elsevier Ltd. All rights reserved.
- Description: 2003011022
On the triality theory for a quartic polynomial optimization problem
- Authors: Gao, David , Wu, Changzhi
- Date: 2012
- Type: Text , Journal article
- Relation: Journal of Industrial and Management Optimization Vol. 8, no. 1 (2012), p. 229-242
- Full Text: false
- Reviewed:
- Description: This paper presents a detailed proof of the triality theorem for a class of fourth-order polynomial optimization problems. The method is based on linear algebra but it solves an open problem on the double-min duality. Results show that the triality theory holds strongly in the tri-duality form for our problem if the primal problem and its canonical dual have the same dimension; otherwise, both the canonical min-max duality and the double-max duality still hold strongly, but the double-min duality holds weakly in a symmetrical form. Some numerical examples are presented to illustrate that this theory can be used to identify not only the global minimum, but also the local minimum and local maximum.
Global optimum design of uniform FIR filter bank with magnitude constraints
- Authors: Wu, Changzhi , Teo, Kok Lay , Rehbock, Volker , Dam, Haihuyen
- Date: 2008
- Type: Text , Journal article
- Relation: IEEE Transactions on Signal Processing Vol. 56, no. 11 (2008), p. 5478-5486
- Full Text: false
- Reviewed:
- Description: The optimum design of a uniform finite impulse response filter bank can be formulated as a nonlinear semi-infinite optimization problem. However, this optimization problem is nonconvex with infinitely many inequality constraints. In this paper, we propose a new hybrid approach for solving this highly challenging nonlinear, nonconvex semi-infinite optimization problem. In this approach, a gradient-based method is used in conjunction with a filled function method to determine a global minimum of the problem. This new hybrid approach finds an optimal result independent of the initial guess of the solution. The method is applied to some existing examples. The results obtained are superior to those obtained by other existing methods. © 2008 IEEE.