On the minimization of possibly discontinuous functions by means of pointwise approximations
A general approach for the solution of possibly discontinuous optimization problems by means of pointwise (perhaps smooth) approximations will be proposed. It will be proved that sequences generated by pointwise approximation techniques eventually satisfy well justified stopping criteria. Numerical examples will be given.
KeywordsDiscontinuous functions Pointwise approximations Smoothing Minimization
The authors would like to thank the associate editor and the three referees for their comments and remarks that helped a lot to improve the first version of this work.
- 1.Abraham, Z., Xin, F., Tan, P.-N.: Smoothed quantile regression for statistical downscaling of extreme events in climate modeling. In: Srivastava, A.N., Chawla, N.V., Perera, A.S. (eds.) Proceedings of the 2011 Conference on Intelligent Data Understanding (CIDU 2011), pp. 92–106. Mountain View, CA (2011)Google Scholar
- 11.Kamimura, K., Nishino, H.: An efficient method for determining economical configurations of elementary packet-switched networks. IEEE Trans. Cybern. 39, 278–288 (1991)Google Scholar