Extended monotropic programming and duality

D. P. Bertsekas

doi:10.1007/s10957-008-9393-3

Extended monotropic programming and duality

D. P. Bertsekas

Research output: Contribution to journal › Article › peer-review

23 Scopus citations

Abstract

We consider the problem min Σ_i=1^m f _i(x_i) s.t. x ε S, 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.

Original language	English (US)
Pages (from-to)	209-225
Number of pages	17
Journal	Journal of Optimization Theory and Applications
Volume	139
Issue number	2
DOIs	https://doi.org/10.1007/s10957-008-9393-3
State	Published - Nov 2008
Externally published	Yes

Keywords

Duality
Monotropic
ε-descent
ε-subdifferential

ASJC Scopus subject areas

Control and Optimization
Applied Mathematics
Management Science and Operations Research

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10.1007/s10957-008-9393-3

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title = "Extended monotropic programming and duality",

abstract = "We consider the problem min Σi=1m f i(xi) s.t. x ε S, where xi are multidimensional subvectors of x, fi are convex functions, and S is a subspace. Monotropic programming, extensively studied by Rockafellar, is the special case where the subvectors xi 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 = "Duality, Monotropic, ε-descent, ε-subdifferential",

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AU - Bertsekas, D. P.

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PY - 2008/11

Y1 - 2008/11

N2 - We consider the problem min Σi=1m f i(xi) s.t. x ε S, where xi are multidimensional subvectors of x, fi are convex functions, and S is a subspace. Monotropic programming, extensively studied by Rockafellar, is the special case where the subvectors xi 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.

AB - We consider the problem min Σi=1m f i(xi) s.t. x ε S, where xi are multidimensional subvectors of x, fi are convex functions, and S is a subspace. Monotropic programming, extensively studied by Rockafellar, is the special case where the subvectors xi 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.

KW - Duality

KW - Monotropic

KW - ε-descent

KW - ε-subdifferential

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Extended monotropic programming and duality

Abstract

Keywords

ASJC Scopus subject areas

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