| 1. |
- Harju, Janne, 1980-, et al.
(författare)
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Utilizing Low Rank Properties when Solving KYP-SDPs
- 2006
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Ingår i: Proceedings of the 45th IEEE Conference on Decision and Control. - Linköping : Linköping University Electronic Press. - 1424401712 ; , s. 5150-5155
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Konferensbidrag (refereegranskat)abstract
- Semidefinite programs and especially those derived from the Kalman-Yakubovich-Popov lemma are quite common in control applications. KYPD is a dedicated solver for KYP-SDPs. It solves the optimization problem via the dual SDP. The solver is iterative. In each step a Hessian is formed and a linear system of equations is solved. The calculations can be performed much faster if we utilize sparsity and low rank structure. We show how to transform a dense optimization problem into a sparse one with low rank structure. A customized calculation of the Hessian is presented and investigated.
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| 2. |
- Vandenberghe, Lieven, et al.
(författare)
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Interior-Point Algorithms for Semidefinite Programming Problems Derived from the KYP Lemma
- 2005
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Ingår i: Positive Polynomials in Control. - Berlin, Heidelberg : Springer Berlin/Heidelberg. - 3540239480 ; , s. 195-238
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Bokkapitel (refereegranskat)abstract
- We discuss fast implementations of primal-dual interior-point methods for semidefinite programs derived from the Kalman-Yakubovich-Popov lemma, a class of problems that are widely encountered in control and signal processing applications. By exploiting problem structure we achieve a reduction of the complexity by several orders of magnitude compared to general-purpose semidefinite programming solvers.
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| 3. |
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| 4. |
- Wallin, Ragnar, 1962-, et al.
(författare)
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A Cutting Plane Method for Solving KYP-SDPs
- 2006
-
Rapport (övrigt vetenskapligt/konstnärligt)abstract
- Semidefinite programs originating from the Kalman-Yakubovich-Popov lemma are convex optimization problems and there exist polynomial time algorithms that solve them. However, the number of variables is often very large making the computational time extremely long. Algorithms more efficient than general purpose solvers are thus needed. To this end structure exploiting algorithms have been proposed, based on the dual formulation. In this paper a cutting plane algorithm is proposed. In a comparison with a general purpose solver and a structure exploiting solver it is shown that the cutting plane based solver can handle optimization problems of much higher dimension.
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| 5. |
- Wallin, Ragnar, 1962-, et al.
(författare)
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A Cutting Plane Method for Solving KYP-SDPs
- 2008
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Ingår i: Automatica. - : Elsevier. - 0005-1098 .- 1873-2836. ; 44:2, s. 418-429
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Tidskriftsartikel (refereegranskat)abstract
- Semidefinite programs originating from the Kalman-Yakubovich-Popov lemma are convex optimization problems and there exist polynomial time algorithms that solve them. However, the number of variables is often very large making the computational time extremely long. Algorithms more efficient than general purpose solvers are thus needed. To this end structure exploiting algorithms have been proposed, based on the dual formulation. In this paper a cutting plane algorithm is proposed. In a comparison with a general purpose solver and a structure exploiting solver it is shown that the cutting plane based solver can handle optimization problems of much higher dimension.
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| 6. |
- Wallin, Ragnar, 1962-, et al.
(författare)
-
A Decomposition Approach for Solving KYP-SDPs
- 2005
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Ingår i: Proceedings of the 16th IFAC World Congress. - 9783902661753 ; , s. 1021-1021
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Konferensbidrag (refereegranskat)abstract
- Semidefinite programs originating from the Kalman-Yakubovich-Popov lemma are convex optimization problems and there exist polynomial time algorithms that solve them. However, the number of variables is often very large making the computational time extremely long. Algorithms more efficient than general purpose solvers are thus needed. In this paper a generalized Benders decomposition algorithm is applied to the problem to improve efficiency.
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| 7. |
- Wallin, Ragnar, et al.
(författare)
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A Structure Exploiting Preprocessor for Semidefinite Programs Derived From the Kalman-Yakubovich-Popov Lemma
- 2009
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Ingår i: IEEE Transactions on Automatic Control. - 0018-9286 .- 1558-2523. ; 54:4, s. 697-704
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Tidskriftsartikel (refereegranskat)abstract
- Semidefinite programs derived from the Kalman-Yakubovich-Popov (KYP) lemma are quite common in control and signal processing applications. The programs are often of high dimension which makes them hard or impossible to solve with general-purpose solvers. Here we present a customized preprocessor, KYPD, that utilizes the inherent structure of this particular optimization problem. The key to an efficient implementation is to transform the optimization problem into an equivalent semidefinite program. This equivalent problem has much fewer variables and the matrices in the linear matrix inequality constraints are of low rank. KYPD can use any primal-dual solver for semidefinite programs as an underlying solver.
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| 8. |
- Wallin, Ragnar, 1962-, et al.
(författare)
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User's Guide to Kypd_Solver
- 2006
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- This package contains software for solving semidefinite programs (SDPs) originating from the Kalman-Yakubovich-Popov lemma. A presentation of the software is given and the options included are presented and described.
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