4 citations · 4 across the 8 of their papers we have counts for
8 papers
Last two pieces of the puzzle for unsolvability of a system of two quadratic (in)equalities
Min-Chi Wang, Ruey-Lin Sheu, Huu-Quang Nguyen
Given two quadratic functions \( f(x) = x^T Ax + 2a^T x + a_0 \) and \( g(x) = x^T Bx + 2b^T x + b_0 ,\) each associated with either the strict inequality (); non-strict inequa…
The Joint Range of Quadratic Mapping on Hilbert Space
Huu-Quang Nguyen
We present a novel technical method for analyzing the hidden convex structure embedded in the joint range of a quadratic mapping defined on a Hilbert space. Our approach stands out…
On the convexity for the range set of two quadratic functions
Huu-Quang Nguyen, Ya-Chi Chu, Ruey-Lin Sheu
Given symmetric matrices and , Dines in 1941 proved that the joint range set is always convex. Our paper is concerned with…
A new separable property of the joint numerical range of quadratic functions and its applications to the Smallest Enclosing Ball Problem
Van-Bong Nguyen, Huu-Quang Nguyen
We explore separable property of the joint numerical range of a special class of quadratic functions and apply it to solving the smallest enclosing ball (SEB) problem…
On Separation of level sets for a pair of quadratic functions
Huu-Quang Nguyen, Ya-Chi Chu, Ruey-Lin Sheu
Given a quadratic function it is possible that its level set has two connected components and thus can be separated by the le…
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 is given as composition of a quadratic function with two -variate q…
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?…
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…