CONVEXIFICATION OF STRICTLY MONOTONE FUNCTIONS

Authors

  • Jenny Rojas Jerónimo
  • Jhon Angulo Viteri

DOI:

https://doi.org/10.17268/sel.mat.2016.02.04

Keywords:

Convexification, monotonicity, nonsmooth functions

Abstract

This paper presents the theory that guarantees the convexification of a strictly monotone function. We proves a theorem and two corollaries for convexification of strictly monotones functions twice continuously differentiable, then the generalization of these results is presented for convexication of nondifferentiable strictly monotones functions. Both cases are exemplars. This results are using in optimization nonsmooth.

References

Bazaraa, M., Programacion Lineal y Flujos y Redes, segunda edición, Noriega Editores, Mexico, 2004.

Bazaraa, M., Nonlinear Programming: Theory and Algorithms, Third edition, Wiley Interscience, New Jersey, 2006.

Clarke, F., Optimization and Nonsmooth Analysis, University of Montreal, New York, 1983.

Chaney, R., Second-Order Directional Derivatives for Nonsmooth Functions, Journal of Mathematical Analysis and Applications 128, 495-511, 1987.

Dara, A. and Dutta, J., Optimality conditions in convex optimization a Finite-Dimensional View, Taylor and Francis Group, London, 2012.

Hofman, K., A Method for Globally Minimizaing Concave Functions Over Convex Sets, Mathematical Programming 20 (1981) 22-32.

Li, D., Sun, X. and McKinnon, K., An Exact Solution Method for Reliability Optimization Problems in Complex Systems, Annals of Operation Research 133, 129-148, 2005.

Sun, X., Luo, H. and Li, D., Convexication of Nonsmooth Monotone Functions, Journal of Optimization Theory and Applications, Vol.132, No 2, 2007.

Sun, X., Mckinnon, H. and Li, D., A Convexication method for a class of global optimization problems with applications to reliability optimization, Journal of Global Optimization 21: 185-199,2001.

Wu, Z., Zhang, L., Bai, F. AND Yang, X., Convexication and Concavication Methods for some Global Optimization Problems, Journal of Systems Science and Complexity, Vol. 17, No. 3, 2004.

Published

2016-12-11

How to Cite

Rojas Jerónimo, J., & Angulo Viteri, J. (2016). CONVEXIFICATION OF STRICTLY MONOTONE FUNCTIONS. Selecciones Matemáticas, 3(02), 83-100. https://doi.org/10.17268/sel.mat.2016.02.04