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Increasing and Lipschitz continuous minimizers in one-dimensional linear-convex systems without constraints: The continuous and the discrete case. (English) Zbl 0860.90126
Summary: We consider a stochastic control model with linear transition law and arbitrary convex cost functions, a far-reaching generalization of the familiar linear quadratic model. Firstly, conditions are given under which the continuous state version has minimizers $$f_n$$ at each stage $$n$$ which are increasing and in addition either right continuous or continuous or Lipschitz continuous with explicitly given Lipschitz constant. For the computationally important discrete version we verify some analoguous properties under stronger assumptions.

##### MSC:
 90C40 Markov and semi-Markov decision processes