<p>In the history of <strong>dynamic programming</strong>  some economic works are considered   pioneering contributions to the theory of dynamic programming (and  in this sense it can be said that they contributed to aerospace research):</p>
<blockquote>
<p>Dynamics programming is no exception to the rule that good ideas have
deep roots. Ancestors to its functional equations can be traced through
the history of mathematics. But the labors that gave birth to the
field of dynamic programming bear recent dates. They include Massé's
study (1946) of water resources; Wald's study (1947) of
sequential decision problem in statistics; a related study by Arrow,
Blackwell and Girshick(1949); a related study of the control of
inventories by Arrow, Harris and Marshack(1951) and by Dvoretsky, Kiefer and Wolfowitz (1952a, 1952b); and the study
by Bellmann (1952) of functional equations.</p>
<p>It was Bellmann that seized upon the principle of optimality and used
it to analyze hundreds of optimizations problems in mathematics,
engineering, economics operation research, and other fields. <span class="math-container">$^1$</span></p>
</blockquote>
<p><strong>Optimal control,</strong> another field of mathematics widely used by economists, and important in engineering and aerospace studies,  has a long history  and had its origins in the <em>calculus of variations</em> in the 17th century.</p>
<p>The calculus of variations was developed further in the 18th century by Euler and Lagrange and in the 19th century by Legendre, Jacobi, Hamilton, and Weierstrass.</p>
<p>A modern version of the optimal control theory, widely used by economists,  is Pontrjagin's contribution and his <em>Maximum Principle</em>, that has its roots in the exigence of overcoming some limitations of the calculus of variations and its application in various fields of engineering and technology, and has nothing to do with economics and the work of economists.</p>
<p>In the famous Pontryagin's book there is no mention of any economic application, but there is an explicit discussion of the connections between his maximum principle and the method of dynamic programming.<span class="math-container">$^2$</span></p>
<p>For a short outline of the history of optimal control see</p>
<p><a href="https://www.sciencedirect.com/science/article/pii/S0377042700004180" rel="nofollow noreferrer">R.W.H. Sargent, Optimal Control</a>.</p>
<p><strong>Operational research and linear programming</strong> had groundbreaking   contributions of some economists as Kantorovich and Koopman, but their development as  separate disciplines was mainly due to military purposes and also to the second World War. For a brief history see:</p>
<p><a href="https://www.britannica.com/topic/operations-research" rel="nofollow noreferrer">https://www.britannica.com/topic/operations-research</a></p>
<hr />
<p><span class="math-container">$^1$</span><sup>Denardo, Eric V., <em>Dynamic Programming</em>, Dover Publications, 1982, p. 3
</sup></p>
<p><span class="math-container">$^2$</span> <sup>L.S. Pontryagin, V.G. Boltyanskii, R.V. Gamkrelidze, E.F. Mischenko,
<em>The Mathematical Theory of Optimal Processes</em>, (Translation by L.W. Neustadt), Pergamon Press,  (1964), p. 67. </sup></p>
<hr />
<p><em><strong>References</strong></em></p>
<p>Arrow K.J., Blackwell D., Girshick M.A. (1949), &quot;Bayes and Minimax Solutions of Sequential Decision Problem&quot;, <em>Econometrica</em>, 17, pp. 214-244.</p>
<p>Arrow K.J., Harris T.E., , Marshack J.(1951)  &quot;Optimal Inventory Policy&quot;, <em>Econometrica</em>, 19,  pp. 250-272.</p>
<p>Dvoretsky A., Kiefer J.,  Wolfowitz J.(1952a), &quot;The Inventory Problem: I. Case of Known Distribution of Demand&quot;, <em>Econometrica</em>, 20, pp. 187-222.</p>
<p>Dvoretsky A., Kiefer J.,  Wolfowitz J.(1952b), &quot;The Inventory Problem: II. Case of Unknown Distribution of Demand&quot;, <em>Econometrica</em>, 20, pp. 451-466.</p>
<p>Massé.P. (1946) <em>Les Réserves et la regulation de l'avenir dans la vie économique</em>, Hermann, Paris.</p>
<p>Wald, A.(1947) , <em>Sequential Analysis</em>, Wiley.</p>

CC BY-SA 4.0
2023-12-09T03:49:34.413Z
Thank you. The survey by Sargent is really great. It's funny because I automatically thought that it was Thomas and then realized it is not. Thomas Sargent  ( as I'm sure you know ) and the rest of the RE ( or is it now DSGE  )  macro community  use optimal control quite a bit.
mark leeds
CC BY-SA 4.0
2023-12-09T03:51:36.517Z
IMO it would ad clarity to this if it was made clear which of these academics were economists and which were mathematicians or something else. Not sure how to classify people like Arrow though.
Giskard
CC BY-SA 4.0
2023-12-09T03:56:18.600Z
It is difficult. A lot of the macro-machinery ( atleast the RE kind. I can't speak outside RE ) was developed by pioneers like Bellman, Pontyagrin, John Muth, Peter Whittle etc.  But what does one call them ? World renown applied mathematicians ? I don't know.
mark leeds
CC BY-SA 4.0
2023-12-09T03:59:03.100Z
I should have included Kalman in above. No idea what he would call himself either.
mark leeds
CC BY-SA 4.0
2023-12-09T10:15:01.520Z
@Giskard The point, as one can see in the references is that there are **works  in economics** that open the path to dynamic programming. Someone can be both an economist and a mathematician, as Kantorovich for linear programming, but they are economists, in that studied economics! Arrow? Someone can doubt that  he is an economist or should be specified who is? Pointrjagin is not an economist, and I said in the answer that his work has nothing to do with economics, economics is not important for the development of optimal control, as one also see in the short accont of R.H. Sargent.
BakerStreet
CC BY-SA 4.0
2023-12-09T10:32:18.913Z
@mark leeds Thank you.  I too made a jump in the chair when I read 'Sargent'. Kalman, as far as I know is not an economist, the question was about economists who dealt with filds relevant for aerospace studies.
BakerStreet
CC BY-SA 4.0
2023-12-09T13:29:54.603Z
@bakerstreet I think that all the people I mentioned ( I'm not so familiar with arrow ) are really scientists who worked on problems that happened to be related to economics but they worked on math problems. Oh, Kalman is DEFINITELY not an economist but all of his KF and control theory stuff is used heavily in RE.
mark leeds
CC BY-SA 4.0
2023-12-09T14:18:24.330Z
Of course, I agree with you there isn’t always a sharp distinction, and someone can be both an economist and a mathematician, some mathematician  dealt  with economics, some economist dealt heavily with mathematics. 
We can just rely on practical criteria as  reputation, I mean how they are usually considered, or what is their academic  curriculum, their main fields of interest, the prizes they won, and so on. Arrow is Nobel laureate in economics, so nobody could say he is not an economist, even if he had a master’s degree in mathematics and then he switched to economics.
BakerStreet
CC BY-SA 4.0
2023-12-09T14:19:17.070Z
Muth is usually considered an economist, Bellman a mathematician who applied his theories to economics, Pontryagin is a mathematician who never said a word about economics, his fundamental book doesn’t even mention economics.
Stephen Smale is well-known as general equilibrium theorist, but what is he? A mathematician or an economist? As he is a Fields medalist (the equivalent of Nobel Prize for mathematics) and a Wolf Premium (the second very important prize in mathematics), he is usually considered a mathematician with an interest in economics.
BakerStreet
CC BY-SA 4.0
2023-12-09T14:22:55.413Z
A lot of rather advanced mathematical tools are used in economics, as calculus of variations or  control theory, but their development was completely independent of economics.
BakerStreet
CC BY-SA 4.0
2023-12-09T17:57:37.643Z
"*Arrow? Someone can doubt that he is an economist or should be specified who is?*" I think it is fair to consider Arrow and people who mainly work on economics economists, but it is hard to deny that his original training was in mathematics, something that made him very capable in economics. In fact, in my narrow personal experience, even today people who are mathematicians by training have a rather large share in mathematical economics/game theory/econometrics departments.
Giskard
CC BY-SA 4.0
2023-12-09T19:18:01.537Z
Yes, I agree, it's what I said, he had a master's degree in mathematics (not a PHD).  And it is true that mathematicians have an advantage in economics.
BakerStreet
CC BY-SA 4.0
2023-12-08T22:10:28.650Z
2023-12-08T23:09:30.040Z
2023-12-08T23:09:30.040Z
BakerStreet
<p>We see the work of Bellman showing up in both orbital trajectory planning/optimization and, obviously DSGE modeling. Also, in a recent example, the JWST uses ideas surrounding Pareto optimization and frontiers to schedule observations most efficiently. Linear programming was also essential for planning and executing tasks for the Apollo missions. These were just a few ideas off the top of my head.</p>
<p>Does anyone have any other way econ has directly contributed to aerospace/space exploration? This could be just a fantasy of mine that some lowly economist saved the day with a novel equation or something.</p>
<p>Edit: I did find this 1963 article written by Bellman. This leads me to believe that at least they were applying these methods simultaneously to economics and aerospace. Surely, there were insights from mathematicians doing economic modeling that crossed the hallway to their colleagues doing aerospace modeling? I think this is the crux of my question. Do we have evidence of this?</p>
<p>Sources:</p>
<p>Multi-Objective Evolutionary Algorithms for Scheduling the
James Webb Space Telescope:
<a href="https://citeseerx.ist.psu.edu/document?repid=rep1&amp;type=pdf&amp;doi=08081b3eee9e7911c93cbe06052cdfef6c4f71a3" rel="nofollow noreferrer">https://citeseerx.ist.psu.edu/document?repid=rep1&amp;type=pdf&amp;doi=08081b3eee9e7911c93cbe06052cdfef6c4f71a3</a></p>
<p>Optimal Earth-Moon Transfer Trajectory Design
via Differential Dynamic Programming with Input Saturation Constraints
<a href="https://www.jstage.jst.go.jp/article/tastj/19/5/19_19.766/_pdf" rel="nofollow noreferrer">https://www.jstage.jst.go.jp/article/tastj/19/5/19_19.766/_pdf</a></p>
<p>Dynamic Programming and Mathematical Economics by Richard Bellman
<a href="https://apps.dtic.mil/sti/tr/pdf/AD0400573.pdf" rel="nofollow noreferrer">https://apps.dtic.mil/sti/tr/pdf/AD0400573.pdf</a></p>

CC BY-SA 4.0
2023-12-08T00:13:04.377Z
Krugman has a paper on [interstellar trade](https://www.princeton.edu/~pkrugman/interstellar.pdf) !
Walrasian Auctioneer
CC BY-SA 4.0
2023-12-08T07:24:49.123Z
"*econ has directly contributed to aerospace/space exploration*"
Do you have any reason to assign Bellman's work or linear programming to economics? I mean it is used in economics, but neither was invented by economists?
I think the Krugman paper is a much better example of economic "contributions" to the field.
Giskard
CC BY-SA 4.0
2023-12-08T19:24:24.757Z
@Giskard, that's a fair concern. I'm not as sure about econ's direct contribution to dynamic programming, though I think there is probably an argument to be made. Huge advances in linear programming were made by Kantorovich, Von Neumann, Dantzig, and Koopmans. I guess it's challenging to delineate what counts in this regard when the tool was developed by mathematicians and simultaneously utilized in multiple fields. 
https://en.wikipedia.org/wiki/Linear_programming
giff
<mathematical-economics><pareto-efficiency><dynamic-programming><dynamic-optimization><linear-programming>
Has mathematical economics contributed to the mathematics of space exploration?
giff
# Has mathematical economics contributed to the mathematics of space exploration?

(Asked by: username_0 on 2023-12-07)

We see the work of Bellman showing up in both orbital trajectory planning/optimization and, obviously DSGE modeling. Also, in a recent example, the JWST uses ideas surrounding Pareto optimization and frontiers to schedule observations most efficiently. Linear programming was also essential for planning and executing tasks for the Apollo missions. These were just a few ideas off the top of my head.

Does anyone have any other way econ has directly contributed to aerospace/space exploration? This could be just a fantasy of mine that some lowly economist saved the day with a novel equation or something.

Edit: I did find this 1963 article written by Bellman. This leads me to believe that at least they were applying these methods simultaneously to economics and aerospace. Surely, there were insights from mathematicians doing economic modeling that crossed the hallway to their colleagues doing aerospace modeling? I think this is the crux of my question. Do we have evidence of this?

Sources:

Multi-Objective Evolutionary Algorithms for Scheduling the
James Webb Space Telescope:
<https://citeseerx.ist.psu.edu/document?repid=rep1&type=pdf&doi=08081b3eee9e7911c93cbe06052cdfef6c4f71a3>

Optimal Earth-Moon Transfer Trajectory Design
via Differential Dynamic Programming with Input Saturation Constraints
<https://www.jstage.jst.go.jp/article/tastj/19/5/19_19.766/_pdf>

Dynamic Programming and Mathematical Economics by Richard Bellman
<https://apps.dtic.mil/sti/tr/pdf/AD0400573.pdf>

**Tags:** mathematical-economics, pareto-efficiency, dynamic-programming, dynamic-optimization, linear-programming

> **Comments:**
> **username_1**: Krugman has a paper on [interstellar trade](https://www.princeton.edu/~pkrugman/interstellar.pdf) !  
> **username_2**: "*econ has directly contributed to aerospace/space exploration*" Do you have any reason to assign Bellman's work or linear programming to economics? I mean it is used in economics, but neither was invented by economists? I think the Krugman paper is a much better example of economic "contributions" to the field.  
> **username_0**: @username_2, that's a fair concern. I'm not as sure about econ's direct contribution to dynamic programming, though I think there is probably an argument to be made. Huge advances in linear programming were made by Kantorovich, Von Neumann, Dantzig, and Koopmans. I guess it's challenging to delineate what counts in this regard when the tool was developed by mathematicians and simultaneously utilized in multiple fields.  https://en.wikipedia.org/wiki/Linear_programming  

---

## 1 answers

### Answer by username_3 on 2023-12-08. Score: 4

In the history of **dynamic programming** some economic works are considered pioneering contributions to the theory of dynamic programming (and in this sense it can be said that they contributed to aerospace research):

> Dynamics programming is no exception to the rule that good ideas have
> deep roots. Ancestors to its functional equations can be traced through
> the history of mathematics. But the labors that gave birth to the
> field of dynamic programming bear recent dates. They include Massé's
> study (1946) of water resources; Wald's study (1947) of
> sequential decision problem in statistics; a related study by Arrow,
> Blackwell and Girshick(1949); a related study of the control of
> inventories by Arrow, Harris and Marshack(1951) and by Dvoretsky, Kiefer and Wolfowitz (1952a, 1952b); and the study
> by Bellmann (1952) of functional equations.
>
> It was Bellmann that seized upon the principle of optimality and used
> it to analyze hundreds of optimizations problems in mathematics,
> engineering, economics operation research, and other fields. $^1$

**Optimal control,** another field of mathematics widely used by economists, and important in engineering and aerospace studies, has a long history and had its origins in the *calculus of variations* in the 17th century.

The calculus of variations was developed further in the 18th century by Euler and Lagrange and in the 19th century by Legendre, Jacobi, Hamilton, and Weierstrass.

A modern version of the optimal control theory, widely used by economists, is Pontrjagin's contribution and his *Maximum Principle*, that has its roots in the exigence of overcoming some limitations of the calculus of variations and its application in various fields of engineering and technology, and has nothing to do with economics and the work of economists.

In the famous Pontryagin's book there is no mention of any economic application, but there is an explicit discussion of the connections between his maximum principle and the method of dynamic programming.$^2$

For a short outline of the history of optimal control see

[R.W.H. Sargent, Optimal Control](https://www.sciencedirect.com/science/article/pii/S0377042700004180).

**Operational research and linear programming** had groundbreaking contributions of some economists as Kantorovich and Koopman, but their development as separate disciplines was mainly due to military purposes and also to the second World War. For a brief history see:

<https://www.britannica.com/topic/operations-research>

---

$^1$Denardo, Eric V., *Dynamic Programming*, Dover Publications, 1982, p. 3

$^2$ L.S. Pontryagin, V.G. Boltyanskii, R.V. Gamkrelidze, E.F. Mischenko,
*The Mathematical Theory of Optimal Processes*, (Translation by L.W. Neustadt), Pergamon Press, (1964), p. 67.

---

***References***

Arrow K.J., Blackwell D., Girshick M.A. (1949), "Bayes and Minimax Solutions of Sequential Decision Problem", *Econometrica*, 17, pp. 214-244.

Arrow K.J., Harris T.E., , Marshack J.(1951) "Optimal Inventory Policy", *Econometrica*, 19, pp. 250-272.

Dvoretsky A., Kiefer J., Wolfowitz J.(1952a), "The Inventory Problem: I. Case of Known Distribution of Demand", *Econometrica*, 20, pp. 187-222.

Dvoretsky A., Kiefer J., Wolfowitz J.(1952b), "The Inventory Problem: II. Case of Unknown Distribution of Demand", *Econometrica*, 20, pp. 451-466.

Massé.P. (1946) *Les Réserves et la regulation de l'avenir dans la vie économique*, Hermann, Paris.

Wald, A.(1947) , *Sequential Analysis*, Wiley.

> **Comments:**
> **username_4**: Thank you. The survey by Sargent is really great. It's funny because I automatically thought that it was Thomas and then realized it is not. Thomas Sargent  ( as I'm sure you know ) and the rest of the RE ( or is it now DSGE  )  macro community  use optimal control quite a bit.  
> **username_2**: IMO it would ad clarity to this if it was made clear which of these academics were economists and which were mathematicians or something else. Not sure how to classify people like Arrow though.  
> **username_4**: It is difficult. A lot of the macro-machinery ( atleast the RE kind. I can't speak outside RE ) was developed by pioneers like Bellman, Pontyagrin, John Muth, Peter Whittle etc.  But what does one call them ? World renown applied mathematicians ? I don't know.  
> **username_4**: I should have included Kalman in above. No idea what he would call himself either.  
> **username_3**: @username_2 The point, as one can see in the references is that there are **works  in economics** that open the path to dynamic programming. Someone can be both an economist and a mathematician, as Kantorovich for linear programming, but they are economists, in that studied economics! Arrow? Someone can doubt that  he is an economist or should be specified who is? Pointrjagin is not an economist, and I said in the answer that his work has nothing to do with economics, economics is not important for the development of optimal control, as one also see in the short accont of R.H. Sargent.  
> **username_3**: @username_4 Thank you.  I too made a jump in the chair when I read 'Sargent'. Kalman, as far as I know is not an economist, the question was about economists who dealt with filds relevant for aerospace studies.  
> **username_4**: @username_3 I think that all the people I mentioned ( I'm not so familiar with arrow ) are really scientists who worked on problems that happened to be related to economics but they worked on math problems. Oh, Kalman is DEFINITELY not an economist but all of his KF and control theory stuff is used heavily in RE.  
> **username_3**: Of course, I agree with you there isn’t always a sharp distinction, and someone can be both an economist and a mathematician, some mathematician  dealt  with economics, some economist dealt heavily with mathematics.  We can just rely on practical criteria as  reputation, I mean how they are usually considered, or what is their academic  curriculum, their main fields of interest, the prizes they won, and so on. Arrow is Nobel laureate in economics, so nobody could say he is not an economist, even if he had a master’s degree in mathematics and then he switched to economics.  
> **username_3**: Muth is usually considered an economist, Bellman a mathematician who applied his theories to economics, Pontryagin is a mathematician who never said a word about economics, his fundamental book doesn’t even mention economics. Stephen Smale is well-known as general equilibrium theorist, but what is he? A mathematician or an economist? As he is a Fields medalist (the equivalent of Nobel Prize for mathematics) and a Wolf Premium (the second very important prize in mathematics), he is usually considered a mathematician with an interest in economics.  
> **username_3**: A lot of rather advanced mathematical tools are used in economics, as calculus of variations or  control theory, but their development was completely independent of economics.  
> **username_2**: "*Arrow? Someone can doubt that he is an economist or should be specified who is?*" I think it is fair to consider Arrow and people who mainly work on economics economists, but it is hard to deny that his original training was in mathematics, something that made him very capable in economics. In fact, in my narrow personal experience, even today people who are mathematicians by training have a rather large share in mathematical economics/game theory/econometrics departments.  
> **username_3**: Yes, I agree, it's what I said, he had a master's degree in mathematics (not a PHD).  And it is true that mathematicians have an advantage in economics.  

---

