RT journal article
T1 Necessary and Sufficient Second-Order Optimality Conditions on Hadamard Manifolds
A1 Ruiz Garzón, Gabriel
A1 Ruiz Zapatero, Jaime
A1 Osuna Gómez, Rafaela
A1 Rufián Lizana, Antonio
A2 Estadística e Investigación Operativa
K1 Hadamard manifold
K1 second-order optimality conditions
K1 generalized convexity
AB This work is intended to lead a study of necessary and sufficient optimality conditions for scalar optimization problems on Hadamard manifolds. In the context of this geometry, we obtain and present new function types characterized by the property of having all their second-order stationary points be global minimums. In order to do so, we extend the concept convexity in Euclidean space to a more general notion of invexity on Hadamard manifolds. This is done employing notions of second-order directional derivatives, second-order pseudoinvexity functions, and the second-order Karush-Kuhn-Tucker-pseudoinvexity problem. Thus, we prove that every second-order stationary point is a global minimum if and only if the problem is either second-order pseudoinvex or second-order KKT-pseudoinvex depending on whether the problem regards unconstrained or constrained scalar optimization, respectively. This result has not been presented in the literature before. Finally, examples of these new characterizations are provided in the context of "Higgs Boson like" potentials, among others.
PB MDPI
SN 2227-7390
YR 2020
FD 2020-07
LK http://hdl.handle.net/10498/23597
UL http://hdl.handle.net/10498/23597
LA eng
DS Repositorio Institucional de la Universidad de Cádiz
RD 12-nov-2026