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Sergei Sergeev

  1. Tropical linear programming and parametric mean payoff games.

    Ср, 01/19/2011 - 16:01 — SomNambul
    Authors: Sergei Sergeev, Stephane Gaubert, Ricardo D. Katz
    Subjects: Metric Geometry
    Abstract

    Tropical polyhedra have been recently used to represent disjunctive
    invariants in static analysis. To handle larger instances, tropical analogues
    of classical linear programming results need to be developed. This motivation
    leads us to study a general tropical linear programming problem.

  2. Basic solutions of systems with two max-linear inequalities.

    Чт, 02/04/2010 - 16:01 — SomNambul
    Authors: Sergei Sergeev, Edouard Wagneur
    Subjects: Rings and Algebras
    Abstract

    We give an explicit description of the basic solutions of max-linear systems
    with two inequalities.

  3. Spectrum of two-sided eigenproblem on max algebra: every system of intervals is realizable.

    Пнд, 01/25/2010 - 16:01 — SomNambul
    Authors: Sergei Sergeev
    Subjects: Rings and Algebras
    Abstract

    We consider the two-sided eigenproblem Ax= lBx over max algebra. It is shown
    that any finite system of real intervals and points can be represented as
    spectrum of this eigenproblem.

  4. CSR expansions of matrix powers in max algebra.

    Втр, 12/15/2009 - 16:01 — SomNambul
    Authors: Sergei Sergeev, Hans Schneider
    Subjects: Rings and Algebras
    Abstract

    We study the behavior of max-algebraic powers of a reducible nonnegative n by
    n matrix A. We show that for t>3n^2, the powers A^t can be expanded in
    max-algebraic powers of the form CS^tR, where C and R are extracted from
    columns and rows of certain Kleene stars and S is diadonally similar to a
    Boolean matrix. We study the properties of individual terms and show that all
    terms, for a given t>3n^2, can be found in O(n^4 log n) operations.

  5. On hyperplanes and semispaces in max-min convex geometry.

    Втр, 10/06/2009 - 17:01 — SomNambul
    Authors: Viorel Nitica, Sergei Sergeev
    Subjects: Metric Geometry
    Abstract

    The concept of separation by hyperplanes is fundamental for convex geometry
    and its tropical (max-plus) analogue. However, analogous separation results in
    max-min convex geometry are based on semispaces. This paper answers the
    question which semispaces are hyperplanes and when it is possible to
    classically separate by hyperplanes in max-min convex geometry.

  6. An interval version of separation by semispaces in max-min convexity.

    Втр, 10/06/2009 - 17:01 — SomNambul
    Authors: Viorel Nitica, Sergei Sergeev
    Subjects: Metric Geometry
    Abstract

    We study separation of a closed box from a max-min convex set by max-min
    semispace. This can be regarded as an interval extension of known separation
    results. We give a constructive proof of the separation in the case when the
    box and the max-min convex set satisfy certain condition, and we show that
    separation is never possible if this condition does not hold. We also study
    separation of max-min convex sets by boxes and by box and semispace.

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