Ya-Chi Chu

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20212025

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math.OC2025

On the convexity for the range set of two quadratic functions

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

Given $n \times n$ symmetric matrices $A$ and $B$ , Dines in 1941 proved that the joint range set ${(x^{T} A x, x^{T} B x) ∣ x \in R^{n}}$ is always convex. Our paper is concerned with…

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…