source/src/refs.bib

% universal approximation
@article{hornik1989multilayer,
  title={Multilayer feedforward networks are universal approximators},
  author={Hornik, Kurt and Stinchcombe, Maxwell and White, Halbert},
  journal={Neural networks},
  volume={2},
  number={5},
  pages={359--366},
  year={1989},
  publisher={Elsevier}
}

@article{pinkus1999approximation,
  title={Approximation theory of the MLP model in neural networks},
  author={Pinkus, Allan},
  journal={Acta numerica},
  volume={8},
  pages={143--195},
  year={1999},
  publisher={Cambridge University Press}
}

@article{yarotsky2022universal,
  title={Universal approximations of invariant maps by neural networks},
  author={Yarotsky, Dmitry},
  journal={Constructive Approximation},
  volume={55},
  number={1},
  pages={407--474},
  year={2022},
  publisher={Springer}
}

@article{bronstein2021geometric,
  title={Geometric deep learning: Grids, groups, graphs, geodesics, and gauges},
  author={Bronstein, Michael M and Bruna, Joan and Cohen, Taco and Veli{\v{c}}kovi{\'c}, Petar},
  journal={arXiv preprint arXiv:2104.13478},
  year={2021}
}

@article{liang2016deep,
  title={Why deep neural networks for function approximation?},
  author={Liang, Shiyu and Srikant, Rayadurgam},
  journal={arXiv preprint arXiv:1610.04161},
  year={2016}
}

@article{lu2021deep,
  title={Deep network approximation for smooth functions},
  author={Lu, Jianfeng and Shen, Zuowei and Yang, Haizhao and Zhang, Shijun},
  journal={SIAM Journal on Mathematical Analysis},
  volume={53},
  number={5},
  pages={5465--5506},
  year={2021},
  publisher={SIAM}
}
% --------
% simple convex
@inproceedings{balazs2015near,
  title={Near-optimal max-affine estimators for convex regression},
  author={Bal{\'a}zs, G{\'a}bor and Gy{\"o}rgy, Andr{\'a}s and Szepesv{\'a}ri, Csaba},
  booktitle={Artificial Intelligence and Statistics},
  pages={56--64},
  year={2015},
  organization={PMLR}
}


@article{magnani2009convex,
  title={Convex piecewise-linear fitting},
  author={Magnani, Alessandro and Boyd, Stephen P},
  journal={Optimization and Engineering},
  volume={10},
  pages={1--17},
  year={2009},
  publisher={Springer}
}

@article{calafiore2019log,
  title={Log-sum-exp neural networks and posynomial models for convex and log-log-convex data},
  author={Calafiore, Giuseppe C and Gaubert, Stephane and Possieri, Corrado},
  journal={IEEE transactions on neural networks and learning systems},
  volume={31},
  number={3},
  pages={827--838},
  year={2019},
  publisher={IEEE}
}


@article{kim2022parameterized,
  title={Parameterized convex universal approximators for decision-making problems},
  author={Kim, Jinrae and Kim, Youdan},
  journal={IEEE Transactions on Neural Networks and Learning Systems},
  volume={35},
  number={2},
  pages={2448--2459},
  year={2022},
  publisher={IEEE}
}
% --------
% complicated convex

@article{warin2023groupmax,
  title={The GroupMax neural network approximation of convex functions},
  author={Warin, Xavier},
  journal={IEEE Transactions on Neural Networks and Learning Systems},
  year={2023},
  publisher={IEEE}
}

@inproceedings{amos2017input,
  title={Input convex neural networks},
  author={Amos, Brandon and Xu, Lei and Kolter, J Zico},
  booktitle={International conference on machine learning},
  pages={146--155},
  year={2017},
  organization={PMLR}
}


% ---------
% gradient

@article{chaudhari2024gradient,
  title={Gradient Networks},
  author={Chaudhari, Shreyas and Pranav, Srinivasa and Moura, Jos{\'e} MF},
  journal={IEEE Transactions on Signal Processing},
  year={2024},
  publisher={IEEE}
}

@article{lorraine2024jacnet,
  title={Jacnet: Learning functions with structured jacobians},
  author={Lorraine, Jonathan and Hossain, Safwan},
  journal={arXiv preprint arXiv:2408.13237},
  year={2024}
}

@article{richter2021input,
  title={Input convex gradient networks},
  author={Richter-Powell, Jack and Lorraine, Jonathan and Amos, Brandon},
  journal={arXiv preprint arXiv:2111.12187},
  year={2021}
}

@article{saremi2019approximating,
  title={On approximating $\nabla f$ with neural networks},
  author={Saremi, Saeed},
  journal={arXiv preprint arXiv:1910.12744},
  year={2019}
}

% --------------------------------------

% functional optimization of convex functions

@article{chen2018optimal,
  title={Optimal control via neural networks: A convex approach},
  author={Chen, Yize and Shi, Yuanyuan and Zhang, Baosen},
  journal={arXiv preprint arXiv:1805.11835},
  year={2018}
}


@article{huang2020convex,
  title={
  Potential flows: Universal probability distributions with optimal transport and convex optimization},
  author={Huang, Chin-Wei and Chen, Ricky TQ and Tsirigotis, Christos and Courville, Aaron},
  journal={arXiv preprint arXiv:2012.05942},
  year={2020}
}

@inproceedings{makkuva2020optimal,
  title={Optimal transport mapping via input convex neural networks},
  author={Makkuva, Ashok and Taghvaei, Amirhossein and Oh, Sewoong and Lee, Jason},
  booktitle={International Conference on Machine Learning},
  pages={6672--6681},
  year={2020},
  organization={PMLR},
}


@article{alvarez2021optimizing,
  title={Optimizing functionals on the space of probabilities with input convex neural networks},
  author={Alvarez-Melis, David and Schiff, Yair and Mroueh, Youssef},
  journal={arXiv preprint arXiv:2106.00774},
  year={2021}
}

% --------------------------------

% abstract convexity

@book{van1993theory,
  title={Theory of convex structures},
  author={van De Vel, Marcel LJ},
  volume={50},
  year={1993},
  publisher={Elsevier}
}

@book{pallaschke2013foundations,
  title={Foundations of mathematical optimization: convex analysis without linearity},
  author={Pallaschke, Diethard Ernst and Rolewicz, Stefan},
  volume={388},
  year={2013},
  publisher={Springer Science \& Business Media}
}

@article{singer1997abstract,
  title={Abstract convex analysis},
  author={Singer, Ivan},
  journal={(No Title)},
  year={1997}
}

@book{rubinov2013abstract,
  title={Abstract convexity and global optimization},
  author={Rubinov, Alexander M},
  volume={44},
  year={2013},
  publisher={Springer Science \& Business Media}
}
% --------------------------------

% mechanism design and numeric optimization

@inproceedings{sandholm2003automated,
  title={Automated mechanism design: A new application area for search algorithms},
  author={Sandholm, Tuomas},
  booktitle={International Conference on Principles and Practice of Constraint Programming},
  pages={19--36},
  year={2003},
  organization={Springer}
}

@inproceedings{shen2020reinforcement,
  title={Reinforcement mechanism design: With applications to dynamic pricing in sponsored search auctions},
  author={Shen, Weiran and Peng, Binghui and Liu, Hanpeng and Zhang, Michael and Qian, Ruohan and Hong, Yan and Guo, Zhi and Ding, Zongyao and Lu, Pengjun and Tang, Pingzhong},
  booktitle={Proceedings of the AAAI conference on artificial intelligence},
  volume={34},
  number={02},
  pages={2236--2243},
  year={2020}
}

@InProceedings{pmlr-v119-deng20d,
  title = 	 {Robust Pricing in Dynamic Mechanism Design},
  author =       {Deng, Yuan and Lahaie, Sebastien and Mirrokni, Vahab},
  booktitle = 	 {Proceedings of the 37th International Conference on Machine Learning},
  pages = 	 {2494--2503},
  year = 	 {2020},
  editor = 	 {III, Hal Daumé and Singh, Aarti},
  volume = 	 {119},
  series = 	 {Proceedings of Machine Learning Research},
  month = 	 {13--18 Jul},
  publisher =    {PMLR},
  pdf = 	 {http://proceedings.mlr.press/v119/deng20d/deng20d.pdf},
  url = 	 {https://proceedings.mlr.press/v119/deng20d.html},
  abstract = 	 {Motivated by the repeated sale of online ads via auctions, optimal pricing in repeated auctions has attracted a large body of research. While dynamic mechanisms offer powerful techniques to improve on both revenue and efficiency by optimizing auctions across different items, their reliance on exact distributional information of buyers’ valuations (present and future) limits their use in practice. In this paper, we proOptimal Transport Networks in Spatial Equilibrium
pose robust dynamic mechanism design. We develop a new framework to design dynamic mechanisms that are robust to both estimation errors in value distributions and strategic behavior. We apply the framework in learning environments, leading to the first policy that achieves provably low regret against the optimal dynamic mechanism in contextual auctions, where the dynamic benchmark has full and accurate distributional information.}
}


@article{balcan2008reducing,
  title={Reducing mechanism design to algorithm design via machine learning},
  author={Balcan, Maria-Florina and Blum, Avrim and Hartline, Jason D and Mansour, Yishay},
  journal={Journal of Computer and System Sciences},
  volume={74},
  number={8},
  pages={1245--1270},
  year={2008},
  publisher={Elsevier}
}
% ---------------------------------

% Mechanism dsign and optimal transport

@article{roberts1979characterization,
  title={The characterization of implementable choice rules},
  author={Roberts, Kevin},
  journal={Aggregation and revelation of preferences},
  volume={12},
  number={2},
  pages={321--348},
  year={1979},
  publisher={North Holland Publishing Company}
}

@article{ashlagi2010monotonicity,
  title={Monotonicity and implementability},
  author={Ashlagi, Itai and Braverman, Mark and Hassidim, Avinatan and Monderer, Dov},
  journal={Econometrica},
  volume={78},
  number={5},
  pages={1749--1772},
  year={2010},
  publisher={Wiley Online Library}
}

@article{rochet1987necessary,
  title={A necessary and sufficient condition for rationalizability in a quasi-linear context},
  author={Rochet, Jean-Charles},
  journal={Journal of mathematical Economics},
  volume={16},
  number={2},
  pages={191--200},
  year={1987},
  publisher={Elsevier}
} 

@article{figalli2011multidimensional,
  title={When is multidimensional screening a convex program?},
  author={Figalli, Alessio and Kim, Young-Heon and McCann, Robert J},
  journal={Journal of Economic Theory},
  volume={146},
  number={2},
  pages={454--478},
  year={2011},
  publisher={Elsevier}
}

% --------------------------------
% metric

@article{torous2024optimal,
  title={An optimal transport approach to estimating causal effects via nonlinear difference-in-differences},
  author={Torous, William and Gunsilius, Florian and Rigollet, Philippe},
  journal={Journal of Causal Inference},
  volume={12},
  number={1},
  pages={20230004},
  year={2024},
  publisher={De Gruyter}
}

@book{kim2024semi,
  title={Semi-nonparametric models of multidimensional matching: an optimal transport approach},
  author={Kim, Dongwoo and Lee, Young Jun},
  year={2024},
  publisher={Cemmap, Centre for Microdata Methods and Practice, The Institute for Fiscal~…}
}

@article{chernozhukov2021identification,
  title={Identification of hedonic equilibrium and nonseparable simultaneous equations},
  author={Chernozhukov, Victor and Galichon, Alfred and Henry, Marc and Pass, Brendan},
  journal={Journal of Political Economy},
  volume={129},
  number={3},
  pages={842--870},
  year={2021},
  publisher={The University of Chicago Press Chicago, IL}
}

@article{ekeland2004identification,
  title={Identification and estimation of hedonic models},
  author={Ekeland, Ivar and Heckman, James J and Nesheim, Lars},
  journal={Journal of political economy},
  volume={112},
  number={S1},
  pages={S60--S109},
  year={2004},
  publisher={The University of Chicago Press}
}

@article{galichon2017survey,
  title={A survey of some recent applications of optimal transport methods to econometrics},
  author={Galichon, Alfred},
  journal={The Econometrics Journal},
  volume={20},
  number={2},
  pages={C1--C11},
  year={2017},
  publisher={Oxford University Press Oxford, UK}
}


@article{dupuy2019estimating,
  title={Estimating matching affinity matrices under low-rank constraints},
  author={Dupuy, Arnaud and Galichon, Alfred and Sun, Yifei},
  journal={Information and Inference: A Journal of the IMA},
  volume={8},
  number={4},
  pages={677--689},
  year={2019},
  publisher={Oxford University Press}
}


% labor
@techreport{boerma2021sorting,
  title={Sorting with team formation},
  author={Boerma, Job and Tsyvinski, Aleh and Zimin, Alexander P},
  year={2021},
  institution={National Bureau of Economic Research}
}


% marriage

@article{becker1973theory,
  title={A theory of marriage: Part I},
  author={Becker, Gary S},
  journal={Journal of Political economy},
  volume={81},
  number={4},
  pages={813--846},
  year={1973},
  publisher={The University of Chicago Press}
}


@article{shapley1971assignment,
  title={The assignment game I: The core},
  author={Shapley, Lloyd S and Shubik, Martin},
  journal={International Journal of game theory},
  volume={1},
  number={1},
  pages={111--130},
  year={1971},
  publisher={Springer}
}

@article{carlier2010matching,
  title={Matching for teams},
  author={Carlier, Guillaume and Ekeland, Ivar},
  journal={Economic theory},
  volume={42},
  pages={397--418},
  year={2010},
  publisher={Springer}
}

% trade

@article{wilson1969use,
  title={The use of entropy maximising models, in the theory of trip distribution, mode split and route split},
  author={Wilson, Alan Geoffrey},
  journal={Journal of transport economics and policy},
  pages={108--126},
  year={1969},
  publisher={JSTOR}
}

@article{silva2006log,
  title={The log of gravity},
  author={Silva, JMC Santos and Tenreyro, Silvana},
  journal={The Review of Economics and statistics},
  pages={641--658},
  year={2006},
  publisher={JSTOR}
}




% hedonic


@article{chiappori2010hedonic,
  title={Hedonic price equilibria, stable matching, and optimal transport: equivalence, topology, and uniqueness},
  author={Chiappori, Pierre-Andr{\'e} and McCann, Robert J and Nesheim, Lars P},
  journal={Economic Theory},
  volume={42},
  pages={317--354},
  year={2010},
  publisher={Springer}
}

@article{ekeland2010existence,
  title={Existence, uniqueness and efficiency of equilibrium in hedonic markets with multidimensional types},
  author={Ekeland, Ivar},
  journal={Economic Theory},
  volume={42},
  number={2},
  pages={275--315},
  year={2010},
  publisher={Springer}
}

% discrete choice
@article{galichon2022cupid,
  title={Cupid’s invisible hand: Social surplus and identification in matching models},
  author={Galichon, Alfred and Salani{\'e}, Bernard},
  journal={The Review of Economic Studies},
  volume={89},
  number={5},
  pages={2600--2629},
  year={2022},
  publisher={Oxford University Press}
}

@article{chiong2016duality,
  title={Duality in dynamic discrete-choice models},
  author={Chiong, Khai Xiang and Galichon, Alfred and Shum, Matt},
  journal={Quantitative Economics},
  volume={7},
  number={1},
  pages={83--115},
  year={2016},
  publisher={Wiley Online Library}
}

% trafic
@article{santambrogio2007transport,
  title={Transport and concentration problems with interaction effects},
  author={Santambrogio, Filippo},
  journal={Journal of Global Optimization},
  volume={38},
  number={1},
  pages={129--141},
  year={2007},
  publisher={Springer}
}

@article{buttazzo2005model,
  title={A model for the optimal planning of an urban area},
  author={Buttazzo, Giuseppe and Santambrogio, Filippo},
  journal={SIAM journal on mathematical analysis},
  volume={37},
  number={2},
  pages={514--530},
  year={2005},
  publisher={SIAM}
}

@article{carlier2005variational,
  title={A variational model for urban planning with traffic congestion},
  author={Carlier, Guillaume and Santambrogio, Filippo},
  journal={ESAIM: Control, Optimisation and Calculus of Variations},
  volume={11},
  number={4},
  pages={595--613},
  year={2005},
  publisher={EDP Sciences}
}

 policy
@article{buttazzo2006optimal,
  title={Optimal pricing policies for public transportation networks},
  author={Buttazzo, Giuseppe and Pratelli, Aldo and Stepanov, Eugene},
  journal={Siam Journal on Optimization},
  volume={16},
  number={3},
  pages={826--853},
  year={2006},
  publisher={SIAM}
}


@article{buttazzo2013optimal,
  title={Optimal spatial pricing strategies with transportation costs},
  author={Buttazzo, Giuseppe and Carlier, Guillaume},
  journal={arXiv preprint arXiv:1312.6500},
  year={2013}
}

@book{buttazzo2008optimal,
  title={Optimal urban networks via mass transportation},
  author={Buttazzo, Giuseppe and Pratelli, Aldo and Solimini, Sergio and Stepanov, Eugene},
  year={2008},
  publisher={Springer Science \& Business Media}
}

@techreport{steinerberger2019tax,
  title={Tax mechanisms and gradient flows},
  author={Steinerberger, Stefan and Tsyvinski, Aleh},
  year={2019},
  institution={National Bureau of Economic Research}
}

% city eq
@article{carlier2007equilibrium,
  title={Equilibrium structure of a bidimensional asymmetric city},
  author={Carlier, Guillaume and Ekeland, Ivar},
  journal={Nonlinear Analysis: Real World Applications},
  volume={8},
  number={3},
  pages={725--748},
  year={2007},
  publisher={Elsevier}
}

@article{fajgelbaum2020optimal,
  title={Optimal transport networks in spatial equilibrium},
  author={Fajgelbaum, Pablo D and Schaal, Edouard},
  journal={Econometrica},
  volume={88},
  number={4},
  pages={1411--1452},
  year={2020},
  publisher={Wiley Online Library}
}

% Principle-Agent

@article{carlier2001general,
  title={A general existence result for the principal-agent problem with adverse selection},
  author={Carlier, Guillaume},
  journal={Journal of Mathematical Economics},
  volume={35},
  number={1},
  pages={129--150},
  year={2001},
  publisher={Elsevier}
}

@article{rochet1998ironing,
  title={Ironing, sweeping, and multidimensional screening},
  author={Rochet, Jean-Charles and Chon{\'e}, Philippe},
  journal={Econometrica},
  pages={783--826},
  year={1998},
  publisher={JSTOR}
}

@article{rochet1985taxation,
  title={The taxation principle and multi-time Hamilton-Jacobi equations},
  author={Rochet, Jean-Charles},
  journal={Journal of Mathematical Economics},
  volume={14},
  number={2},
  pages={113--128},
  year={1985},
  publisher={Elsevier}
}

@inproceedings{daskalakis2013mechanism,
  title={Mechanism design via optimal transport},
  author={Daskalakis, Constantinos and Deckelbaum, Alan and Tzamos, Christos},
  booktitle={Proceedings of the fourteenth ACM conference on Electronic commerce},
  pages={269--286},
  year={2013}
}

@inproceedings{daskalakis2015strong,
  title={Strong duality for a multiple-good monopolist},
  author={Daskalakis, Constantinos and Deckelbaum, Alan and Tzamos, Christos},
  booktitle={Proceedings of the Sixteenth ACM Conference on Economics and Computation},
  pages={449--450},
  year={2015}
}

@article{kolesnikov2022beckmann,
  title={Beckmann's approach to multi-item multi-bidder auctions},
  author={Kolesnikov, Alexander V and Sandomirskiy, Fedor and Tsyvinski, Aleh and Zimin, Alexander P},
  journal={arXiv preprint arXiv:2203.06837},
  year={2022}
}


% persuasion
@article{kolotilin2022persuasion,
  title={Persuasion with non-linear preferences},
  author={Kolotilin, Anton and Corrao, Roberto and Wolitzky, Alexander},
  journal={arXiv preprint arXiv:2206.09164},
  year={2022}
}

@article{arieli2023persuasion,
  title={Persuasion as transportation},
  author={Arieli, Itai and Babichenko, Yakov and Sandomirskiy, Fedor},
  journal={arXiv preprint arXiv:2307.07672},
  year={2023}
}

@article{lin2024credible,
  title={Credible persuasion},
  author={Lin, Xiao and Liu, Ce},
  journal={Journal of Political Economy},
  volume={132},
  number={7},
  pages={2228--2273},
  year={2024},
  publisher={The University of Chicago Press Chicago, IL}
}

@article{malamud2021persuasion,
  title={Persuasion by dimension reduction},
  author={Malamud, Semyon and Schrimpf, Andreas},
  journal={arXiv preprint arXiv:2110.08884},
  year={2021}
}

@article{cieslak2021optimal,
  title={Optimal transport of information},
  author={Cieslak, Anna and Malamud, Semyon and Schrimpf, Andreas},
  year={2021},
  publisher={CEPR Discussion Paper No. DP15859}
}











% -------------------------------------------
% misc


@article{lecun1989backpropagation,
  title={Backpropagation applied to handwritten zip code recognition},
  author={LeCun, Yann and Boser, Bernhard and Denker, John S and Henderson, Donnie and Howard, Richard E and Hubbard, Wayne and Jackel, Lawrence D},
  journal={Neural computation},
  volume={1},
  number={4},
  pages={541--551},
  year={1989},
  publisher={MIT Press}
}


@article{fan2020scalable,
  title={Scalable computations of wasserstein barycenter via input convex neural networks},
  author={Fan, Jiaojiao and Taghvaei, Amirhossein and Chen, Yongxin},
  journal={arXiv preprint arXiv:2007.04462},
  year={2020}
}


@article{chen2018neural,
  title={Neural ordinary differential equations},
  author={Chen, Ricky TQ and Rubanova, Yulia and Bettencourt, Jesse and Duvenaud, David K},
  journal={Advances in neural information processing systems},
  volume={31},
  year={2018}
}



% ----------------------------
% single crossing
@article{mirrlees1971exploration,
  title={An exploration in the theory of optimum income taxation},
  author={Mirrlees, James A},
  journal={The review of economic studies},
  volume={38},
  number={2},
  pages={175--208},
  year={1971},
  publisher={Wiley-Blackwell}
}

@incollection{spence1978job,
  title={Job market signaling},
  author={Spence, Michael},
  booktitle={Uncertainty in economics},
  pages={281--306},
  year={1978},
  publisher={Elsevier}
}


@article{brenier1991polar,
  title={Polar factorization and monotone rearrangement of vector-valued functions},
  author={Brenier, Yann},
  journal={Communications on pure and applied mathematics},
  volume={44},
  number={4},
  pages={375--417},
  year={1991},
  publisher={Wiley Online Library}
}

@article{ekeland2010notes,
  title={Notes on optimal transportation},
  author={Ekeland, Ivar},
  journal={Economic Theory},
  pages={437--459},
  year={2010},
  publisher={JSTOR}
}

@book{cannarsa2004semiconcave,
  title={Semiconcave Functions, Hamilton—Jacobi Equations, and Optimal Control},
  author={Cannarsa, Piermarco and Sinestrari, Carlo},
  year={2004},
  publisher={Springer}
}



@article{armstrong1996multiproduct,
  title={Multiproduct nonlinear pricing},
  author={Armstrong, Mark},
  journal={Econometrica: Journal of the Econometric Society},
  pages={51--75},
  year={1996},
  publisher={JSTOR}
}


@article{manelli2006bundling,
  title={Bundling as an optimal selling mechanism for a multiple-good monopolist},
  author={Manelli, Alejandro M and Vincent, Daniel R},
  journal={Journal of Economic Theory},
  volume={127},
  number={1},
  pages={1--35},
  year={2006},
  publisher={Elsevier}
}

@article{manelli2007multidimensional,
  title={Multidimensional mechanism design: Revenue maximization and the multiple-good monopoly},
  author={Manelli, Alejandro M and Vincent, Daniel R},
  journal={Journal of Economic theory},
  volume={137},
  number={1},
  pages={153--185},
  year={2007},
  publisher={Elsevier}
}

@inproceedings{giannakopoulos2014duality,
  title={Duality and optimality of auctions for uniform distributions},
  author={Giannakopoulos, Yiannis and Koutsoupias, Elias},
  booktitle={Proceedings of the fifteenth ACM conference on Economics and computation},
  pages={259--276},
  year={2014}
}

@article{joswig2022generalized,
  title={Generalized permutahedra and optimal auctions},
  author={Joswig, Michael and Klimm, Max and Spitz, Sylvain},
  journal={SIAM Journal on Applied Algebra and Geometry},
  volume={6},
  number={4},
  pages={711--739},
  year={2022},
  publisher={SIAM}
}