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Convex optimization approach to a single quadratically constrained quadratic minimization problem

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  • Maziar Salahi

Abstract

In this paper, first we show that for rank deficient matrices, the optimal solution of a single equality constrained quadratic minimization problem can be found by relaxing the equality constraint to the inequality one, which makes the problem a convex problem. Then we show that for full rank matrices, an optimal solution can be obtained using semidefinite optimization framework. Copyright Springer-Verlag 2010

Suggested Citation

  • Maziar Salahi, 2010. "Convex optimization approach to a single quadratically constrained quadratic minimization problem," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 18(2), pages 181-187, June.
    • Handle: RePEc:spr:cejnor:v:18:y:2010:i:2:p:181-187
    DOI: 10.1007/s10100-009-0106-2
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    References listed on IDEAS

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    1. de Klerk, E., 2006. "The Complexity of Optimizing over a Simplex, Hypercube or Sphere : A Short Survey," Discussion Paper 2006-85, Tilburg University, Center for Economic Research.
    2. Etienne Klerk, 2008. "The complexity of optimizing over a simplex, hypercube or sphere: a short survey," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 16(2), pages 111-125, June.
    3. Sturm, J.F. & Zhang, S., 2001. "On Cones of Nonnegative Quadratic Functions," Other publications TiSEM 075a6b4d-5b51-4153-a9c3-0, Tilburg University, School of Economics and Management.
    4. de Klerk, E., 2008. "The complexity of optimizing over a simplex, hypercube or sphere : A short survey," Other publications TiSEM 485b6860-cf1d-4cad-97b8-2, Tilburg University, School of Economics and Management.
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    Cited by:

    1. Balázs Lévai & Balázs Bánhelyi, 2013. "An optimization technique for verified location of trajectories with prescribed geometrical behaviour in the chaotic forced damped pendulum," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 21(4), pages 757-767, December.

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