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.
ASJC Scopus subject areas
- Control and Optimization
- Management Science and Operations Research
- Applied Mathematics