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
no code implementations • VLSP 2020 • Duc-Trong Le, Xuan-Son Vu, Nhu-Dung To, Huu-Quang Nguyen, Thuy-Trinh Nguyen, Linh Le, Anh-Tuan Nguyen, Minh-Duc Hoang, Nghia Le, Huyen Nguyen, Hoang D. Nguyen
This paper reports on the ReINTEL Shared Task for Responsible Information Identification on social network sites, which is hosted at the seventh annual workshop on Vietnamese Language and Speech Processing (VLSP 2020).
