Ruey-Lin Sheu

collaborators

4 papers

math.OC2021

On Separation of level sets for a pair of quadratic functions

Huu-Quang Nguyen, Ya-Chi Chu, Ruey-Lin Sheu

Given a quadratic function $f (x) = x^{T} A x + 2 a^{T} x + a_{0},$ it is possible that its level set ${x \in R^{n} : f (x) = 0}$ has two connected components and thus can be separated by the le…

math.OC2020

Solving a new type of quadratic optimization problem having a joint numerical range constraint

Huu-Quang Nguyen, Ruey-Lin Sheu, Yong Xia

We propose a new formulation of quadratic optimization problems. The objective function $F (f (x), g (x))$ is given as composition of a quadratic function $F (z)$ with two $n$ -variate q…

math.OC2020

Deciding whether two quadratic surfaces actually intersect

Huu-Quang Nguyen, Ruey-Lin Sheu, Yong Xia

We answer an open question proposed by Pólik and Terlaky in 2007 that: {\it how we can decide whether two quadratic surfaces intersect without actually computing the intersections?…

math.OC2020

Arrangement of level sets of quadratic constraints and its relation to nonconvex quadratic optimization problems

Huu-Quang Nguyen, Ruey-Lin Sheu

We study a special class of non-convex quadratic programs subject to two (possibly indefinite) quadratic constraints when the level sets of the constraint functions are {\it not} a…