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Extended Monotropic Programming and Duality

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  • D. P. Bertsekas

    (M.I.T.)

Abstract

We consider the problem $$\begin{array}{l@{\quad}l}\mbox{min}&\displaystyle\sum_{i=1}^{m}f_{i}(x_{i}),\\[12pt]\mbox{s.t.}&x\in S,\end{array}$$ where x i are multidimensional subvectors of x, f i are convex functions, and S is a subspace. Monotropic programming, extensively studied by Rockafellar, is the special case where the subvectors x i are the scalar components of x. We show a strong duality result that parallels Rockafellar’s result for monotropic programming, and contains other known and new results as special cases. The proof is based on the use of ε-subdifferentials and the ε-descent method, which is used here as an analytical vehicle.

Suggested Citation

  • D. P. Bertsekas, 2008. "Extended Monotropic Programming and Duality," Journal of Optimization Theory and Applications, Springer, vol. 139(2), pages 209-225, November.
    • Handle: RePEc:spr:joptap:v:139:y:2008:i:2:d:10.1007_s10957-008-9393-3
    DOI: 10.1007/s10957-008-9393-3
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    Cited by:

    1. R. I. Boţ & E. R. Csetnek, 2010. "On a Zero Duality Gap Result in Extended Monotropic Programming," Journal of Optimization Theory and Applications, Springer, vol. 147(3), pages 473-482, December.

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