Earlier and Recent Results on Convex Mappings and Convex Optimization


Octav Olteanu

The main purpose of this review-paper is to recall and partially prove earlier, as well as recent results on
convex optimization, published by the author in the last decades. Examples are given along the article. Some
of these results have been published recently. Most of theorems have a clear geometric meaning. Minimum
norm elements are characterized in normed vector spaces framework. Distanced convex subsets and related
parallel hyperplanes preserving the distance are also discussed. The convex involved objective-mappings are
real valued or take values in an order-complete vector lattice. On the other side, an optimization problem
related to Markov moment problem is solved in the end.


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