On the spherical quasi-convexity of quadratic functions
O. P. Ferreira, S. Z. N\'emeth, L. Xiao
TL;DR
This paper investigates the conditions under which quadratic functions are spherical quasi-convex on convex sets, providing characterizations and specific conditions for the spherical positive orthant, with illustrative examples.
Contribution
It offers new characterizations and conditions for the spherical quasi-convexity of quadratic functions, especially on the spherical positive orthant.
Findings
Conditions characterizing spherical quasi-convexity are established.
Specific conditions for quadratic functions on the spherical positive orthant are provided.
Examples illustrate the theoretical results.
Abstract
In this paper the spherical quasi-convexity of quadratic functions on spherically convex sets is studied. Several conditions characterizing the spherical quasi-convexity of quadratic functions are presented. In particular, conditions implying spherical quasi-convexity of quadratic functions on the spherical positive orthant are given. Some examples are provided as an application of the obtained results.
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Taxonomy
TopicsMathematical Inequalities and Applications · Analytic and geometric function theory · Optimization and Variational Analysis