Result: Mathematical properties of optimization problems defined by positively homogeneous functions

Title:
Mathematical properties of optimization problems defined by positively homogeneous functions
Source:
Journal of optimization theory and applications. 112(1):31-52
Publisher Information:
New York, NY: Springer, 2002.
Publication Year:
2002
Physical Description:
print, 15 ref
Original Material:
CRAN
Document Type:
Academic journal Article
File Description:
text
Language:
English
Author Affiliations:
LAAS-CNRS, Toulouse, France
Département de Mathématiques, Université Paul Sabatier, Toulouse, France
ISSN:
0022-3239
Rights:
CC BY 4.0
Sauf mention contraire ci-dessus, le contenu de cette notice bibliographique peut être utilisé dans le cadre d’une licence CC BY 4.0 Inist-CNRS / Unless otherwise stated above, the content of this bibliographic record may be used under a CC BY 4.0 licence by Inist-CNRS / A menos que se haya señalado antes, el contenido de este registro bibliográfico puede ser utilizado al amparo de una licencia CC BY 4.0 Inist-CNRS
Notes:
Mathematics
Accession Number:
edscal.14246909
Database:
PASCAL Archive

Further Information

We consider the nonlinear programming problem (J)→{min f(x)|gl(x)≤bi, i = 1,…,m}, with f positively p-homogeneous and gi positively q-homogeneous functions. We show that (J) admits a simple min-max formulation (D) with the inner max-problem being a trivial linear program with a single constraint. This provides a new formulation of the linear programming problem and the linear-quadratic one as well. In particular, under some conditions, a global (nonconvex) optimization problem with quadratic data is shown to be equivalent to a convex minimization problem.