How should I think about the differences between stochastic optimization (SO) and stochastic programming (SP)? From Wikipedia, it seems that SO is a framework that uses randomness to solve a pre-existing optimization problem whereas SP uses randomness to formulate an optimization problem.

Is this accurate? What am I missing?


Currently, I think that Wikipedia's distinction between SO and SP is a nice categorization of "method" and "formulation", respectively. In light of this distinction, I feel that robust optimization (RO) might be better named "robust programming" (RP).

Now I'm trying to understand the philosphical differences between SP and RP. It seems that SP makes use of probabilistic tools to work with explicit (distributional form) representations of uncertainty whereas RP assumes makes no explicit use of probabilistic tools outside of assuming known support for an uncertainty set $\mathcal{U}$. Is this the primary distinction? Is there a way to view RP as a subclass of SP problems?

  • $\begingroup$ Stochastic optimization is the bigger field of study where stochastic programming follows specific models $\endgroup$ – User2648648 Dec 9 '17 at 1:34
  • $\begingroup$ Thanks @User2648648, can you elaborate and maybe provide an example of what you mean by specific models in SP (and perhaps the more general concept explored in SO)? From Wikipedia, it seems that SO deals more with methods whereas SP deals more with a particular problem / program formulation $\endgroup$ – jjjjjj Dec 9 '17 at 1:35
  • $\begingroup$ The basic feature that differs stochastic programming problems from other optimization problems is the way in which the objective function or constraint functions are defined. In stochastic programming problems values of some of these functions are numerical characteristics of random phenomena dependent on the decision variables. $\endgroup$ – User2648648 Dec 9 '17 at 1:43
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    $\begingroup$ Heres a link to a book that provides some good examples: pure.iiasa.ac.at/3065/1/XB-88-403.pdf $\endgroup$ – User2648648 Dec 9 '17 at 1:44
  • $\begingroup$ Thanks for the text! So I understand that SP generalizes traditional deterministic optimization problems, but from the ToC of the book, it seems like SO is concerned with the methods used to numerically solve an existing SP model? $\endgroup$ – jjjjjj Dec 9 '17 at 1:47

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