Abstract
If a nonconvex minimization problem can be converted into an equivalent convex minimization problem, the primal nonconvex minimization problem is called a hidden convex minimization problem. Sufficient conditions are developed in this paper to identify such hidden convex minimization problems. Hidden convex minimization problems possess the same desirable property as convex minimization problems: Any lo- cal minimum is also a global minimum. Identification of hidden convex minimization problem extends the reach of global optimization.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
M. Avriel (1976), Nonlinear Programming: Analysis and Methods, Prentice Hall, Englewood Cliffs, N.J.
R. Horst (1984), On the convexification of nonlinear programming problems: An applications-oriented survey, European Journal of Operations Research, 15, pp. 382–392.
D. Li, X. L. Sun, M. P. Biswal and F. Gao (2001), Convexification, concavification and monotonization in global optimization, Annals of Operations Research, 105, pp. 213–226.
D. Li, Z. Wu, H. W. J. Lee, X. Yang and L. Zhang (2003), Hidden convex minimization, to appear in Journal of Global Optimization, 2003.
Sun, X. L., McKinnon, K. and Li, D. (2001), A convexification method for a class of global optimization problem with application to reliability optimization, Journal of Global Optimization, 21, pp. 185–199.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2005 Springer Science + Business Media, Inc.
About this paper
Cite this paper
Li, D., Wu, Z., Lee, H.W.J., Yang, X., Zhang, L. (2005). Identification of Hidden Convex Minimization Problems. In: Eberhard, A., Hadjisavvas, N., Luc, D.T. (eds) Generalized Convexity, Generalized Monotonicity and Applications. Nonconvex Optimization and Its Applications, vol 77. Springer, Boston, MA. https://doi.org/10.1007/0-387-23639-2_17
Download citation
DOI: https://doi.org/10.1007/0-387-23639-2_17
Publisher Name: Springer, Boston, MA
Print ISBN: 978-0-387-23638-4
Online ISBN: 978-0-387-23639-1
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)