Abstract
We establish necessary and sufficient conditions for strong duality of extended monotropic optimization problems with possibly infinite sum of separable functions. The results are applied to a minimization problem of the infinite sum of proper convex functions. We consider a truncation method for duality and obtain the zero duality gap by using only dual variable of finite support. An application to minimum cost flow problems in infinite networks is also discussed.
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To Marco Lopez on occasion of his 70th birthday
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Luc, D.T., Volle, M. Duality for extended infinite monotropic optimization problems. Math. Program. 189, 409–432 (2021). https://doi.org/10.1007/s10107-020-01557-3
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DOI: https://doi.org/10.1007/s10107-020-01557-3