Applied Mathematics & Optimization

, Volume 77, Issue 2, pp 377–404 | Cite as

Two Approaches to Stochastic Optimal Control Problems with a Final-Time Expectation Constraint

  • Laurent PfeifferEmail author


In this article, we study and compare two approaches to solving stochastic optimal control problems with an expectation constraint on the final state. The case of a probability constraint is included in this framework. The first approach is based on a dynamic programming principle and the second one uses Lagrange relaxation. In this article, we focus on discrete-time problems, but the two discussed approaches can be applied to discretized continuous-time problems.


Stochastic optimal control Expectation and probability constraints Dynamic programming Lagrange relaxation 

Mathematics Subject Classification

90C15 93E20 



The author thanks J. Frédéric Bonnans for his advice and the two anonymous referees for useful remarks. The research leading to these results has received funding from the Gaspard Monge Program for Optimization and operations research (PGMO). The author gratefully acknowledges the Austrian Science Fund (FWF) for financial support under SFB F32, “Mathematical Optimization and Applications in Biomedical Sciences”.


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Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  1. 1.Institute for Mathematics and Scientific ComputingKarl-Franzens-UniversitätGrazAustria

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