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\bibitem{singer1997abstract}
I.~Singer, ``Abstract convex analysis,'' \emph{(No Title)}, 1997.

\bibitem{hornik1989multilayer}
K.~Hornik, M.~Stinchcombe, and H.~White, ``Multilayer feedforward networks are
  universal approximators,'' \emph{Neural networks}, vol.~2, no.~5, pp.
  359--366, 1989.

\bibitem{pinkus1999approximation}
A.~Pinkus, ``Approximation theory of the mlp model in neural networks,''
  \emph{Acta numerica}, vol.~8, pp. 143--195, 1999.

\bibitem{liang2016deep}
S.~Liang and R.~Srikant, ``Why deep neural networks for function
  approximation?'' \emph{arXiv preprint arXiv:1610.04161}, 2016.

\bibitem{lu2021deep}
J.~Lu, Z.~Shen, H.~Yang, and S.~Zhang, ``Deep network approximation for smooth
  functions,'' \emph{SIAM Journal on Mathematical Analysis}, vol.~53, no.~5,
  pp. 5465--5506, 2021.

\bibitem{lecun1989backpropagation}
Y.~LeCun, B.~Boser, J.~S. Denker, D.~Henderson, R.~E. Howard, W.~Hubbard, and
  L.~D. Jackel, ``Backpropagation applied to handwritten zip code
  recognition,'' \emph{Neural computation}, vol.~1, no.~4, pp. 541--551, 1989.

\bibitem{yarotsky2022universal}
D.~Yarotsky, ``Universal approximations of invariant maps by neural networks,''
  \emph{Constructive Approximation}, vol.~55, no.~1, pp. 407--474, 2022.

\bibitem{bronstein2021geometric}
M.~M. Bronstein, J.~Bruna, T.~Cohen, and P.~Veli{\v{c}}kovi{\'c}, ``Geometric
  deep learning: Grids, groups, graphs, geodesics, and gauges,'' \emph{arXiv
  preprint arXiv:2104.13478}, 2021.

\bibitem{balazs2015near}
G.~Bal{\'a}zs, A.~Gy{\"o}rgy, and C.~Szepesv{\'a}ri, ``Near-optimal max-affine
  estimators for convex regression,'' in \emph{Artificial Intelligence and
  Statistics}.\hskip 1em plus 0.5em minus 0.4em\relax PMLR, 2015, pp. 56--64.

\bibitem{calafiore2019log}
G.~C. Calafiore, S.~Gaubert, and C.~Possieri, ``Log-sum-exp neural networks and
  posynomial models for convex and log-log-convex data,'' \emph{IEEE
  transactions on neural networks and learning systems}, vol.~31, no.~3, pp.
  827--838, 2019.

\bibitem{kim2022parameterized}
J.~Kim and Y.~Kim, ``Parameterized convex universal approximators for
  decision-making problems,'' \emph{IEEE Transactions on Neural Networks and
  Learning Systems}, vol.~35, no.~2, pp. 2448--2459, 2022.

\bibitem{warin2023groupmax}
X.~Warin, ``The groupmax neural network approximation of convex functions,''
  \emph{IEEE Transactions on Neural Networks and Learning Systems}, 2023.

\bibitem{amos2017input}
B.~Amos, L.~Xu, and J.~Z. Kolter, ``Input convex neural networks,'' in
  \emph{International conference on machine learning}.\hskip 1em plus 0.5em
  minus 0.4em\relax PMLR, 2017, pp. 146--155.

\bibitem{magnani2009convex}
A.~Magnani and S.~P. Boyd, ``Convex piecewise-linear fitting,''
  \emph{Optimization and Engineering}, vol.~10, pp. 1--17, 2009.

\bibitem{saremi2019approximating}
S.~Saremi, ``On approximating $\nabla f$ with neural networks,'' \emph{arXiv
  preprint arXiv:1910.12744}, 2019.

\bibitem{chaudhari2024gradient}
S.~Chaudhari, S.~Pranav, and J.~M. Moura, ``Gradient networks,'' \emph{IEEE
  Transactions on Signal Processing}, 2024.

\bibitem{richter2021input}
J.~Richter-Powell, J.~Lorraine, and B.~Amos, ``Input convex gradient
  networks,'' \emph{arXiv preprint arXiv:2111.12187}, 2021.

\bibitem{lorraine2024jacnet}
J.~Lorraine and S.~Hossain, ``Jacnet: Learning functions with structured
  jacobians,'' \emph{arXiv preprint arXiv:2408.13237}, 2024.

\bibitem{chen2018neural}
R.~T. Chen, Y.~Rubanova, J.~Bettencourt, and D.~K. Duvenaud, ``Neural ordinary
  differential equations,'' \emph{Advances in neural information processing
  systems}, vol.~31, 2018.

\bibitem{chen2018optimal}
Y.~Chen, Y.~Shi, and B.~Zhang, ``Optimal control via neural networks: A convex
  approach,'' \emph{arXiv preprint arXiv:1805.11835}, 2018.

\bibitem{huang2020convex}
C.-W. Huang, R.~T. Chen, C.~Tsirigotis, and A.~Courville, ``Potential flows:
  Universal probability distributions with optimal transport and convex
  optimization,'' \emph{arXiv preprint arXiv:2012.05942}, 2020.

\bibitem{makkuva2020optimal}
A.~Makkuva, A.~Taghvaei, S.~Oh, and J.~Lee, ``Optimal transport mapping via
  input convex neural networks,'' in \emph{International Conference on Machine
  Learning}.\hskip 1em plus 0.5em minus 0.4em\relax PMLR, 2020, pp. 6672--6681.

\bibitem{alvarez2021optimizing}
D.~Alvarez-Melis, Y.~Schiff, and Y.~Mroueh, ``Optimizing functionals on the
  space of probabilities with input convex neural networks,'' \emph{arXiv
  preprint arXiv:2106.00774}, 2021.

\bibitem{van1993theory}
M.~L. van De~Vel, \emph{Theory of convex structures}.\hskip 1em plus 0.5em
  minus 0.4em\relax Elsevier, 1993, vol.~50.

\bibitem{pallaschke2013foundations}
D.~E. Pallaschke and S.~Rolewicz, \emph{Foundations of mathematical
  optimization: convex analysis without linearity}.\hskip 1em plus 0.5em minus
  0.4em\relax Springer Science \& Business Media, 2013, vol. 388.

\bibitem{rubinov2013abstract}
A.~M. Rubinov, \emph{Abstract convexity and global optimization}.\hskip 1em
  plus 0.5em minus 0.4em\relax Springer Science \& Business Media, 2013,
  vol.~44.

\bibitem{shen2020reinforcement}
W.~Shen, B.~Peng, H.~Liu, M.~Zhang, R.~Qian, Y.~Hong, Z.~Guo, Z.~Ding, P.~Lu,
  and P.~Tang, ``Reinforcement mechanism design: With applications to dynamic
  pricing in sponsored search auctions,'' in \emph{Proceedings of the AAAI
  conference on artificial intelligence}, vol.~34, no.~02, 2020, pp.
  2236--2243.

\bibitem{pmlr-v119-deng20d}
\BIBentryALTinterwordspacing
Y.~Deng, S.~Lahaie, and V.~Mirrokni, ``Robust pricing in dynamic mechanism
  design,'' in \emph{Proceedings of the 37th International Conference on
  Machine Learning}, ser. Proceedings of Machine Learning Research, H.~D. III
  and A.~Singh, Eds., vol. 119.\hskip 1em plus 0.5em minus 0.4em\relax PMLR,
  13--18 Jul 2020, pp. 2494--2503. [Online]. Available:
  \url{https://proceedings.mlr.press/v119/deng20d.html}
\BIBentrySTDinterwordspacing

\bibitem{balcan2008reducing}
M.-F. Balcan, A.~Blum, J.~D. Hartline, and Y.~Mansour, ``Reducing mechanism
  design to algorithm design via machine learning,'' \emph{Journal of Computer
  and System Sciences}, vol.~74, no.~8, pp. 1245--1270, 2008.

\bibitem{mirrlees1971exploration}
J.~A. Mirrlees, ``An exploration in the theory of optimum income taxation,''
  \emph{The review of economic studies}, vol.~38, no.~2, pp. 175--208, 1971.

\bibitem{spence1978job}
M.~Spence, ``Job market signaling,'' in \emph{Uncertainty in economics}.\hskip
  1em plus 0.5em minus 0.4em\relax Elsevier, 1978, pp. 281--306.

\bibitem{brenier1991polar}
Y.~Brenier, ``Polar factorization and monotone rearrangement of vector-valued
  functions,'' \emph{Communications on pure and applied mathematics}, vol.~44,
  no.~4, pp. 375--417, 1991.

\bibitem{ekeland2010notes}
I.~Ekeland, ``Notes on optimal transportation,'' \emph{Economic Theory}, pp.
  437--459, 2010.

\bibitem{cannarsa2004semiconcave}
P.~Cannarsa and C.~Sinestrari, \emph{Semiconcave Functions, Hamilton—Jacobi
  Equations, and Optimal Control}.\hskip 1em plus 0.5em minus 0.4em\relax
  Springer, 2004.

\bibitem{armstrong1996multiproduct}
M.~Armstrong, ``Multiproduct nonlinear pricing,'' \emph{Econometrica: Journal
  of the Econometric Society}, pp. 51--75, 1996.

\bibitem{rochet1998ironing}
J.-C. Rochet and P.~Chon{\'e}, ``Ironing, sweeping, and multidimensional
  screening,'' \emph{Econometrica}, pp. 783--826, 1998.

\bibitem{manelli2006bundling}
A.~M. Manelli and D.~R. Vincent, ``Bundling as an optimal selling mechanism for
  a multiple-good monopolist,'' \emph{Journal of Economic Theory}, vol. 127,
  no.~1, pp. 1--35, 2006.

\bibitem{manelli2007multidimensional}
------, ``Multidimensional mechanism design: Revenue maximization and the
  multiple-good monopoly,'' \emph{Journal of Economic theory}, vol. 137, no.~1,
  pp. 153--185, 2007.

\bibitem{giannakopoulos2014duality}
Y.~Giannakopoulos and E.~Koutsoupias, ``Duality and optimality of auctions for
  uniform distributions,'' in \emph{Proceedings of the fifteenth ACM conference
  on Economics and computation}, 2014, pp. 259--276.

\bibitem{joswig2022generalized}
M.~Joswig, M.~Klimm, and S.~Spitz, ``Generalized permutahedra and optimal
  auctions,'' \emph{SIAM Journal on Applied Algebra and Geometry}, vol.~6,
  no.~4, pp. 711--739, 2022.

\end{thebibliography}