Properties of the Level Sets of Some Products of Functions
Journal of convex analysis, Tome 30 (2023) no. 1, pp. 271-294
We are interested about pairs $(f,g)$ of $C^2$-smooth functions $f,g:\mathbb{R}^n\longrightarrow\mathbb{R}$ with bounded ${\rm Hess}^+$ complements such that their product preserves this property as well. Recall that ${\rm Hess}^+(f)$ stands for the set of all points $p\in\mathbb{R}^n$ such that the Hessian matrix $H_p(f)$ of the $C^2$-smooth function $f\colon \mathbb{R}^n\longrightarrow\mathbb{R}$ is positive definite. In this paper we consider two pairs of real-valued functions with empty ${\rm Hess}^+$ complements whose products happen to have bounded ${\rm Hess}^+$ complements.
Classification :
47H05, 47H99
Mots-clés : Level curves, Lagrange multipliers, Hessian matrix, curvature
Mots-clés : Level curves, Lagrange multipliers, Hessian matrix, curvature
@article{JCA_2023_30_1_JCA_2023_30_1_a14,
author = {A. Brojbeanu and C. Pintea},
title = {Properties of the {Level} {Sets} of {Some} {Products} of {Functions}},
journal = {Journal of convex analysis},
pages = {271--294},
year = {2023},
volume = {30},
number = {1},
url = {http://geodesic.mathdoc.fr/item/JCA_2023_30_1_JCA_2023_30_1_a14/}
}
A. Brojbeanu; C. Pintea. Properties of the Level Sets of Some Products of Functions. Journal of convex analysis, Tome 30 (2023) no. 1, pp. 271-294. http://geodesic.mathdoc.fr/item/JCA_2023_30_1_JCA_2023_30_1_a14/