no code implementations • 18 Dec 2020 • Huu-Quang Nguyen, Ruey-Lin Sheu, Yong Xia
The objective function $F(f(x), g(x))$ is given as composition of a quadratic function $F(z)$ with two $n$-variate quadratic functions $z_1=f(x)$ and $z_2=g(x).$ In addition, it incorporates with a set of linear inequality constraints in $z=(z_1, z_2)^T,$ while having an implicit constraint that $z$ belongs to the joint numerical range of $(f, g).$ The formulation is very general in the sense that it covers quadratic programming with a single quadratic constraint of all types, including the inequality-type, the equality-type, and the interval-type.
Optimization and Control 90C20, 90C22, 90C26 F.2
no code implementations • 18 Dec 2020 • Huu-Quang Nguyen, Ruey-Lin Sheu, Yong Xia
We answer an open question proposed by P\'{o}lik and Terlaky in 2007 that: {\it how we can decide whether two quadratic surfaces intersect without actually computing the intersections?}
Optimization and Control 90C20, 90C22, 90C26 F.2
no code implementations • 18 Dec 2020 • Huu-Quang Nguyen, Ruey-Lin Sheu
In this paper, we study some fundamental geometrical properties related to level sets of pair of quadratic functions $(g, f)$.
Optimization and Control Classical Analysis and ODEs 90C20, 90C22, 90C26 F.2
