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We show in this paper that a one-layer feedforward neural network with exponential activation functions in the inner layer and logarithmic activation in the output neuron is an universal approximator of convex functions.
J. Kingman, “A convexity property of positive matrices,” Quart. J. Math. Oxford
1961
Earlier work this paper cites.
D. W. Marquardt, “An algorithm for least-squares estimation of nonlinear parameters,” J. Soc. Ind. Appl. Math
1963
Earlier work this paper cites.
J. Wiley & Sons, 1967
R. J. Duffin, E. L. Peterson, and C. M. Zener, Geometric programming: theory and application · 1967
Earlier work this paper cites.
Princeton Univ. Press, 1970
R. T. Rockafellar, Convex Analysis · 1970
Earlier work this paper cites.
C. J. Jachimowski, “Chemical kinetic reaction mechanism for the combustion of propane,” Combustion and Flame
1984
Earlier work this paper cites.
Springer, 1985
L. Scales, Introduction to non-linear optimization · 1985
Earlier work this paper cites.
G. Cybenko, “Approximation by superpositions of a sigmoidal function,” Math. Control Signals Syst
1989
Earlier work this paper cites.
K. Hornik, M. Stinchcombe, and H. White, “Multilayer feedforward networks are universal approximators,” Neural networks
1989
Earlier work this paper cites.
H. White, “Connectionist nonparametric regression: Multilayer feedforward networks can learn arbitrary mappings,” Neural networks
1990
Earlier work this paper cites.
D. W. Ruck, S. K. Rogers, M. Kabrisky, M. E. Oxley, and B. W. Suter, “The multilayer perceptron as an approximation to a Bayes optimal discriminant function,” IEEE Trans. Neural Networks
1990
Earlier work this paper cites.
K. Hornik, “Approximation capabilities of multilayer feedforward networks,” Neural Networks
1991
Earlier work this paper cites.
R. T. Rockafellar, “Lagrange multipliers and optimality,” SIAM Review
1993
Earlier work this paper cites.
Hermann, 1993
L. Schwartz, Topologie générale et analyse fonctionnelle · 1993
Earlier work this paper cites.
Grundlehren der mathematischen Wissenschaften 306, Springer-Verlag Berlin Heidelberg, 1 ed., 1993
C. L. a. Jean-Baptiste Hiriart-Urruty, Convex Analysis and Minimization Algorithms II: Advanced Theory and Bundle Methods · 1993
Earlier work this paper cites.
V. T. S. Elanayar and Y. C. Shin, “Radial basis function neural network for approximation and estimation of nonlinear stochastic dynamic systems,” IEEE Trans. Neural Networks
1994
Earlier work this paper cites.
International Organization for Standardization, “Mechanical Vibration and shock – Evaluation of human exposure to whole-body vibration,” Standard ISO 2631-1:1997(E), May 1997
1997
Cited alongside, same era.
C. Possieri and A. R. Teel, “Stochastic robust simulation and stability properties of chemical reaction networks,” IEEE Trans. Control Network Syst
1997
Cited alongside, same era.
F. A. Potra and S. J. Wright, “Interior-point methods,” J. Comput. Appl. Math
2000
Cited alongside, same era.
O. Viro, “Dequantization of real algebraic geometry on logarithmic paper,” in European Congress of Mathematics, Vol. I (Barcelona, 2000)
2001
Cited alongside, same era.
W. Daems, G. Gielen, and W. Sansen, “Simulation-based generation of posynomial performance models for the sizing of analog integrated circuits,” IEEE Trans. Comput. Aided Des. Integr. Circuits Syst
Springer, 2010
J. Borwein and A. S. Lewis, Convex analysis and nonlinear optimization: theory and examples · 2010
Later among the works it cites.
B. Klartag and E. Milman, “Centroid bodies and the logarithmic Laplace transform–a unified approach,” J. Funct. Anal
2012
Later among the works it cites.
S. H. Zareh, A. Sarrafan, A. A. A. Khayyat, and A. Zabihollah, “Intelligent semi-active vibration control of eleven degrees of freedom suspension system using magnetorheological dampers,” J. Mech. Sci. Technol
2012
Later among the works it cites.
I. Sutskever, J. Martens, G. Dahl, and G. Hinton, “On the importance of initialization and momentum in deep learning,” in Int. Conf. Mach. Learn
2013
Later among the works it cites.
Cambridge Univ. Press, 2014
G. C. Calafiore and L. El Ghaoui, Optimization models · 2014
Later among the works it cites.
alphaXiv searches the wider corpus for related work and actual follow-ups.
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2003
Cited alongside, same era.
Cambridge University Press, 2004
S. Boyd and L. Vandenberghe, Convex optimization · 2004
Cited alongside, same era.
Oberwolfach seminars, Birkhäuser, 2007
I. Itenberg, G. Mikhalkin, and E. Shustin, Tropical algebraic geometry · 2007
Cited alongside, same era.
G. L. Litvinov, “Maslov dequantization, idempotent and tropical mathematics: A brief introduction,” Journal of Mathematical Sciences
2007
Cited alongside, same era.
S. Boyd, S.-J. Kim, L. Vandenberghe, and A. Hassibi, “A tutorial on geometric programming,” Optim. Eng
2007
Cited alongside, same era.
John Wiley & Sons, 2008
A. Forrester, A. Sobester, and A. Keane, Engineering design via surrogate modelling: a practical guide · 2008
Cited alongside, same era.
M. Grant and S. Boyd, “Graph implementations for nonsmooth convex programs,” in Recent Advances in Learning and Control
2008
Cited alongside, same era.
A. Magnani and S. P. Boyd, “Convex piecewise-linear fitting,” Optim. Eng
2009
Cited alongside, same era.
P. Andras, “Function approximation using combined unsupervised and supervised learning,” IEEE Trans. Neural Networks Learn. Syst
2014
Later among the works it cites.
AMS, 2014
S. Brazitikos, A. Giannopoulos, P. Valettas, and B.-H. Vritsiou, Geometry of Isotropic Convex Bodies · 2014
Later among the works it cites.
M. Grant and S. Boyd, “CVX: Matlab software for disciplined convex programming, version 2.1.” http://cvxr.com/cvx , Mar. 2014
2014
Later among the works it cites.
G. C. Calafiore, L. M. El Ghaoui, and C. Novara, “Sparse identification of posynomial models,” Automatica
2015
Later among the works it cites.
W. Hoburg, P. Kirschen, and P. Abbeel, “Data fitting with geometric-programming-compatible softmax functions,” Optim. Eng
2016
Later among the works it cites.
V. Charisopoulos and P. Maragos, “Morphological perceptrons: Geometry and training algorithms,” in Mathematical Morphology and Its Applications to Signal and Image Processing
2017
Later among the works it cites.
R. Yondoa, E. Andrés, and E. Valeroa, “A review on design of experiments and surrogate models in aircraft real-time and many-query aerodynamic analyses,” Progress in Aerospace Sciences
2018
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To appear
L. Zhang, G. Naitzat, and L.-H. Lim, “Tropical geometry of deep neural networks,” in Proceedings of the 35th International Conference on Machine Learning, Stockholm, Sweden, PMLR 80, 2018 · 2018
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The MathWorks Inc
M. H. Beale, M. T. Hagan, and H. B. Demuth, “Neural Network Toolbox User’s Guide,” 2018 · 2018
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