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
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- 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
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- 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.