Extended Monotropic Programming and Duality

D. P. Bertsekas ()
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D. P. Bertsekas: M.I.T.

Journal of Optimization Theory and Applications, 2008, vol. 139, issue 2, No 1, 209-225

Abstract: 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.

Keywords: Monotropic; Duality; ε-subdifferential; ε-descent (search for similar items in EconPapers)
Date: 2008
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s10957-008-9393-3

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