Rational approximation theory occupies a significant place in signal processing and systems theory. This research paper proposes an optimal design of BIBO stable multidimensional Infinite Impulse Response filters with...Rational approximation theory occupies a significant place in signal processing and systems theory. This research paper proposes an optimal design of BIBO stable multidimensional Infinite Impulse Response filters with a realizable (rational) transfer function thanks to the Adamjan, Arov and Krein (AAK) theorem. It is well known that the one dimensional AAK results give the best approximation of a polynomial as a rational function in the Hankel semi norm. We suppose that the Hankel matrix associated to the transfer function has a finite rank.展开更多
We propose a multidimensional filter SQP algorithm.The multidimensional filter technique proposed by Gould et al.[SIAM J.Optim.,2005]is extended to solve constrained optimization problems.In our proposed algorithm,the...We propose a multidimensional filter SQP algorithm.The multidimensional filter technique proposed by Gould et al.[SIAM J.Optim.,2005]is extended to solve constrained optimization problems.In our proposed algorithm,the constraints are partitioned into several parts,and the entry of our filter consists of these different parts.Not only the criteria for accepting a trial step would be relaxed,but the individual behavior of each part of constraints is considered.One feature is that the undesirable link between the objective function and the constraint violation in the filter acceptance criteria disappears.The other is that feasibility restoration phases are unnecessary because a consistent quadratic programming subproblem is used.We prove that our algorithm is globally convergent to KKT points under the constant positive generators(CPG)condition which is weaker than the well-known Mangasarian-Fromovitz constraint qualification(MFCQ)and the constant positive linear dependence(CPLD).Numerical results are presented to show the efficiency of the algorithm.展开更多
文摘Rational approximation theory occupies a significant place in signal processing and systems theory. This research paper proposes an optimal design of BIBO stable multidimensional Infinite Impulse Response filters with a realizable (rational) transfer function thanks to the Adamjan, Arov and Krein (AAK) theorem. It is well known that the one dimensional AAK results give the best approximation of a polynomial as a rational function in the Hankel semi norm. We suppose that the Hankel matrix associated to the transfer function has a finite rank.
基金This work is supported by National Science Founda-tion of China(No.11601318)Equipment Manufacturing Systems and Optimization(No.13XKJC01).
文摘We propose a multidimensional filter SQP algorithm.The multidimensional filter technique proposed by Gould et al.[SIAM J.Optim.,2005]is extended to solve constrained optimization problems.In our proposed algorithm,the constraints are partitioned into several parts,and the entry of our filter consists of these different parts.Not only the criteria for accepting a trial step would be relaxed,but the individual behavior of each part of constraints is considered.One feature is that the undesirable link between the objective function and the constraint violation in the filter acceptance criteria disappears.The other is that feasibility restoration phases are unnecessary because a consistent quadratic programming subproblem is used.We prove that our algorithm is globally convergent to KKT points under the constant positive generators(CPG)condition which is weaker than the well-known Mangasarian-Fromovitz constraint qualification(MFCQ)and the constant positive linear dependence(CPLD).Numerical results are presented to show the efficiency of the algorithm.
