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  • 1.
    Kiwiel, Krzysztof C.
    et al.
    Systems Research Institute, Warszawa.
    Larsson, Torbjörn
    Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Optimization .
    Lindberg, Per Olov
    Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Optimization .
    Lagrangian relaxation via ballstep subgradient methods2007In: Mathematics of Operations Research, ISSN 0364-765X, E-ISSN 1526-5471, Vol. 32, no 3, p. 669-686Article in journal (Refereed)
    Abstract [en]

    We exhibit useful properties of ballstep subgradient methods for convex optimization using level controls for estimating the optimal value. Augmented with simple averaging schemes, they asymptotically find objective and constraint subgradients involved in optimality conditions. When applied to Lagrangian relaxation of convex programs, they find both primal and dual solutions, and have practicable stopping criteria. Up until now, similar results have only been known for proximal bundle methods, and for subgradient methods with divergent series stepsizes, whose convergence can be slow. Encouraging numerical results are presented for large-scale nonlinear multicommodity network flow problems. ©2007 INFORMS.

  • 2.
    Krishnamurthy, Vikram
    et al.
    University of British Columbia.
    Wahlberg, Bo
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Partially Observed Markov Decision Process Multiarmed Bandits-Structural Results2009In: Mathematics of Operations Research, ISSN 0364-765X, E-ISSN 1526-5471, Vol. 34, no 2, p. 287-302Article in journal (Refereed)
    Abstract [en]

    This paper considers multiarmed bandit problems involving partially observed Markov decision processes (POMDPs). We show how the Gittins index for the optimal scheduling policy can be computed by a value iteration algorithm on each process, thereby considerably simplifying the computational cost. A suboptimal value iteration algorithm based on Lovejoy's approximation is presented. We then show that for the case of totally positive of order 2 (TP2) transition probability matrices and monotone likelihood ratio (MLR) ordered observation probabilities, the Gittins index is MLR increasing in the information state. Algorithms that exploit this structure are then presented.

  • 3. Riener, Cordian
    et al.
    Theobald, Thorsten
    Jansson Andren, Lina
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Lasserre, Jean B.
    Exploiting Symmetries in SDP-Relaxations for Polynomial Optimization2013In: Mathematics of Operations Research, ISSN 0364-765X, E-ISSN 1526-5471, Vol. 38, no 1, p. 122-141Article in journal (Refereed)
    Abstract [en]

    In this paper we study various approaches for exploiting symmetries in polynomial optimization problems within the framework of semidefinite programming relaxations. Our special focus is on constrained problems especially when the symmetric group is acting on the variables. In particular, we investigate the concept of block decomposition within the framework of constrained polynomial optimization problems, show how the degree principle for the symmetric group can be computationally exploited, and also propose some methods to efficiently compute the geometric quotient.

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