Piecewise convexity of artificial neural networks

W. I. Zangwill, Nonlinear programming : a unified approach, Prentice-Hall international series in management, Prentice-Hall, Englewood Cliffs, N.J., 1969

1969

Earlier work this paper cites.

R. T. Rockafellar, Convex Analysis, Princeton University Press, 1970

1970

Earlier work this paper cites.

doi:10.1287/opre.24.4.643

R. E. Wendell, A. P. Hurter, Minimization of a non-separable objective function subject to disjoint constraints , Operations Research 24 (4) (1976) 643–657 · 1976

Earlier work this paper cites.

R. Johnsonbaugh, W. E. Pfaffenberger, Foundations of Mathematical Analysis, Marcel Dekker, New York, New York, USA, 1981

1981

Earlier work this paper cites.

doi:10.1016/S0893-6080(05)80010-3

A. L. Blum, R. L. Rivest, Training a 3-node neural network is np-complete, Neural Networks 5 (1) (1992) 117–127 · 1992

Earlier work this paper cites.

doi:10.1023/A:1017979506314

I. Tsevendorj, Piecewise-convex maximization problems, Journal of Global Optimization 21 (1) (2001) 1–14 · 2001

Earlier work this paper cites.

S. Ovchinnikov, Max-min representation of piecewise linear functions, Contributions to Algebra and Geometry 43 (1) (2002) 297–302

2002

Cited alongside, same era.

A. N. Iusem, On the convergence properties of the projected gradient method for convex optimization, Computational and Applied Mathematics 22 (2003) 37 – 52

2003

Cited alongside, same era.

S. Boyd, L. Vandenberghe, Convex Optimization, Cambridge University Press, The Edinburgh Building, Cambridge, CB2 8RU, UK, 2004

2004

Cited alongside, same era.

Y. Nesterov, Introductory Lectures on Convex Optimization : A Basic Course, Applied optimization, Kluwer Academic Publishers, Boston, Dordrecht, London, 2004

2004

Cited alongside, same era.

doi:10.1007/s00186-007-0161-1

J. Gorski, F. Pfeuffer, K. Klamroth, Biconvex sets and optimization with biconvex functions: a survey and extensions, Mathematical Methods of Operations Research 66 (3) (2007) 373–407 · 2007

Cited alongside, same era.

D. P. Bertsekas, Incremental gradient, subgradient, and proximal methods for convex optimization: A survey , Tech. rep., Massachusetts Institute of Technology Labratory for Information and Decision Systems (2010). URL http://arxiv.org/abs/1507.01030

Original

2010

Later among the works it cites.

X. Glorot, A. Bordes, Y. Bengio, Deep sparse rectifier neural networks, in: G. J. Gordon, D. B. Dunson (Eds.), Proceedings of the Fourteenth International Conference on Artificial Intelligence and Statistics (AISTATS-11), Vol. 15, Journal of Machine Learning Research - Workshop and Conference Proceedings, 2011, pp. 315–323

2011

Later among the works it cites.

F. R. Bach, E. Moulines, Non-asymptotic analysis of stochastic approximation algorithms for machine learning, in: Proceedings of the 25th Annual Conference on Neural Information Processing Systems, 2011, pp. 451–459

2011

Later among the works it cites.

doi:10.1016/j.neunet.2012.04.011

P. Baldi, Z. Lu, Complex-valued autoencoders , Neural Networks 33 (2012) 136–147 · 2012

Later among the works it cites.