Semi-bounded quadratic functions over a sublevel set of another quadratic function (Nonlinear Analysis and Convex Analysis)

Abstract

Before attempting to solve an optimization problem, it is important to detect whether the optimal value is finite. This is called the boundedness problem. A function f is called semi-bounded if it is either bounded from below or bounded from above. In this article, we apply the separation peoperty developed by Nguyen and Sheu [10] to study the semi-boundedness of a quadratic fucntion f over the sublevel set {xin mathbb{R}^{n}|g(x)leq 0} of another quadratic function g.