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  • 1.
    Harju, Janne
    et al.
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Wallin, Ragnar
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Hansson, Anders
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Utilizing low rank properties when solving KYP-SDPs2006Rapport (Övrigt vetenskapligt)
    Abstract [en]

    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

    Ladda ner fulltext (pdf)
    FULLTEXT01
  • 2.
    Harju, Janne
    et al.
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Wallin, Ragnar
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Hansson, Anders
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Utilizing Low Rank Properties when Solving KYP-SDPs2006Ingår i: Proceedings of the 45th IEEE Conference on Decision and Control, 2006, s. 5150-5155Konferensbidrag (Refereegranskat)
    Abstract [en]

    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.

  • 3.
    Harju Johansson, Janne
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    A Structure Utilizing Inexact: Primal-Dual Interior-Point Method for Analysis of Linear Differential Inclusions2008Licentiatavhandling, monografi (Övrigt vetenskapligt)
    Abstract [en]

    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.

    Ladda ner fulltext (pdf)
    FULLTEXT01
    Ladda ner (pdf)
    COVER01
  • 4.
    Harju Johansson, Janne
    et al.
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Hansson, Anders
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    A Tailored Inexact Interior-Point Method for Systems Analysis2008Ingår i: Proceedings of Reglermöte 2008, 2008, s. 176-181Konferensbidrag (Övrigt vetenskapligt)
    Abstract [en]

    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.

  • 5.
    Harju Johansson, Janne
    et al.
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Hansson, Anders
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    A Tailored Inexact Interior-Point Method for Systems Analysis2008Rapport (Övrigt vetenskapligt)
    Abstract [en]

    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.

    Ladda ner fulltext (pdf)
    FULLTEXT01
  • 6.
    Harju Johansson, Janne
    et al.
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Hansson, Anders
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    A Tailored Inexact Interior-Point Method for Systems Analysis2008Ingår i: Proceedings of the 47th IEEE Conference on Decision and Control, 2008, s. 3071-3076Konferensbidrag (Refereegranskat)
    Abstract [en]

    Within the area of systems analysis there are several problem formulations that can be rewritten as semidefinite programs. Increasing demand on computational efficiency and ability to solve large scale problems make the available generic solvers inadequate. In this paper structure knowledge is utilized to derive tailored calculations and to incorporate adaptation to the different properties that appear in a proposed inexact interior-point method.

  • 7.
    Harju Johansson, Janne
    et al.
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Hansson, Anders
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    An Inexact Interior-Point Method for Semi-Definite Programming, a Description and Convergence Proof2007Rapport (Övrigt vetenskapligt)
    Abstract [en]

    In this report we investigate convergence for an infeasible interior-point method for semidefinite programming.

    Ladda ner fulltext (pdf)
    FULLTEXT01
  • 8.
    Harju Johansson, Janne
    et al.
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Hansson, Anders
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    An Inexact Interior-Point Method for System Analysis2010Ingår i: International Journal of Control, ISSN 0020-7179, E-ISSN 1366-5820, Vol. 83, nr 3, s. 601-616Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    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.

    Ladda ner fulltext (pdf)
    FULLTEXT01
  • 9.
    Harju Johansson, Janne
    et al.
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Hansson, Anders
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Structure Exploitation in Semi-Definite Programs for Systems Analysis2008Rapport (Övrigt vetenskapligt)
    Abstract [en]

    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.

    Ladda ner fulltext (pdf)
    FULLTEXT01
  • 10.
    Harju Johansson, Janne
    et al.
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Hansson, Anders
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Structure Exploitation in Semi-Definite Programs for Systems Analysis2008Ingår i: Proceedings of the 17th IFAC World Congress, 2008, s. 10045-10050Konferensbidrag (Refereegranskat)
    Abstract [en]

    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.

  • 11.
    Wallin, Ragnar
    et al.
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Hansson, Anders
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Harju Johansson, Janne
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    A Structure Exploiting Preprocessor for Semidefinite Programs Derived From the Kalman-Yakubovich-Popov Lemma2009Ingår i: IEEE Transactions on Automatic Control, ISSN 0018-9286, E-ISSN 1558-2523, Vol. 54, nr 4, s. 697-704Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    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.

  • 12.
    Wallin, Ragnar
    et al.
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Harju, Janne
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    User's Guide to Kypd_Solver2006Rapport (Övrigt vetenskapligt)
    Abstract [en]

    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.

    Ladda ner fulltext (pdf)
    FULLTEXT01
1 - 12 av 12
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  • apa
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  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
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