| 1. |
- Harju Johansson, Janne, 1980-
(författare)
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A Structure Utilizing Inexact : Primal-Dual Interior-Point Method for Analysis of Linear Differential Inclusions
- 2008
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Licentiatavhandling (övrigt vetenskapligt/konstnärligt)abstract
- The ability to analyze system properties for large scale systems is an important part of modern engineering. Although computer power increases constantly, there is still need to develop tailored methods that are able to handle large scale systems, since sometimes standard methods cannot handle the large scale problems that occur.In this thesis the focus is on system analysis, in particular analysis methods that result in optimization problems with a specific problem structure. In order to solve these optimization problems, primal-dual interior-point methods have been tailored to the specific structure. A convergence proof for the suggested algorithm is also presented.It is the structure utilization and the use of an iterative solver for the search directions that enables the algorithm to be applied to optimization problems with a large number of variables. However, the use of an iterative solver to find the search directions will give infeasible iterates in the optimization algorithm. This make the use of an infeasible method desirable and hence is such a method proposed.Using an iterative solver requires a good preconditioner. In this work two different preconditioners are used for different stages of the algorithm. The first preconditioner is used in the initial stage, while the second preconditioner is applied when the iterates of the algorithm are close to the boundary of the feasible set.The proposed algorithm is evaluated in a simulation study. It is shown that problems which are unsolvable for a standard solver are solved by the proposed algorithm.
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| 2. |
- Harju Johansson, Janne, et al.
(författare)
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A Tailored Inexact Interior-Point Method for Systems Analysis
- 2008
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Ingår i: Proceedings of Reglermöte 2008. - Linköping : Linköping University Electronic Press. ; , s. 176-181, s. 3071-3076
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Konferensbidrag (övrigt vetenskapligt/konstnärligt)abstract
- Within the area of system analysis there are multiple problem formulations that can be rewritten as semidefiniteprograms. Increasing demand on computational efficiency andability to solve large scale problems make the available genericsolvers inadequate. In this paper structure knowledge is utilizedto derive tailored calculations and to incorporate adaptationto the different properties that appear in a proposed inexactinterior-point method.
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| 3. |
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| 4. |
- Harju Johansson, Janne, et al.
(författare)
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An Inexact Interior-Point Method for System Analysis
- 2010
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Ingår i: International Journal of Control. - : Taylor & Francis. - 0020-7179 .- 1366-5820. ; 83:3, s. 601-616
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Tidskriftsartikel (refereegranskat)abstract
- In this article, a primal-dual interior-point algorithm for semidefinite programming that can be used for analysing e.g. polytopic linear differential inclusions is tailored in order to be more computationally efficient. The key to the speedup is to allow for inexact search directions in the interior-point algorithm. These are obtained by aborting an iterative solver for computing the search directions prior to convergence. A convergence proof for the algorithm is given. Two different preconditioners for the iterative solver arc proposed. The speedup is in many cases more than an order of magnitude. Moreover, the proposed algorithm can be used to analyse much larger problems as compared to what is possible with off-the-shelf interior-point solvers.
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| 5. |
- Harju Johansson, Janne, 1980-, et al.
(författare)
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Structure Exploitation in Semi-Definite Programs for Systems Analysis
- 2008
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Ingår i: Proceedings of the 17th IFAC World Congress. - Linköping : Linköping University Electronic Press. ; , s. 10045-10050
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Konferensbidrag (refereegranskat)abstract
- A wide variety of problems involving analysis of systems can be rewritten as a semidefinite program. When solving these problems optimization algorithms are used. Large size makes the problems unsolvable in practice and computationally more effective solvers are needed. This paper investigates how to exploit structure and problem knowledge in some control applications. It is shown that inexact search directions are useful to reduce the computational burden and that operator formalism can be utilized to derive tailored calculations.
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| 6. |
- 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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