62 citations · 124 across the 15 of their papers we have counts for
15 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…
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…
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…
Simultaneous diagonalization via congruence of real symmetric matrices and its implications in optimization
Thi-Ngan Nguyen, Van-Bong Nguyen, Thanh-Hieu Le +1
Let be a collection of real symmetric matrices. The objective of the paper is to offer an algorithm that finds a common congruence ma…
Double Well Potential Function and Its Optimization in The n-dimensional Real Space -- Part I
Shu-Cherng Fang, David Yang Gao, Gang-Xuan Lin +2
A special type of multi-variate polynomial of degree 4, called the double well potential function, is studied. When the function is bounded from below, it has a very unique propert…
On the p-regularized trust region subproblem
Yong Hsia, Ruey-Lin Sheu, Ya-xiang Yuan
The -regularized subproblem (p-RS) is a regularisation technique in computing a Newton-like step for unconstrained optimization, which globally minimizes a local quadratic appro…
Double Well Potential Function and Its Optimization in the n-dimensional Real Space - Part II
Yong Xia, Ruey-Lin Sheu, Shu-Cherng Fang +1
In contrast to taking the dual approach for finding a global minimum solution of a double well potential function, in Part II of the paper, we characterize a local minimizer, local…
S-Lemma with Equality and Its Applications
Yong Xia, Shu Wang, Ruey-Lin Sheu
Let and be two quadratic functions having symmetric matrices and . The S-lemma with equality asks when the unsolvability of the sys…
An SDP Approach For Solving Quadratic Fractional Programming Problems
Van-Bong Nguyen, Ruey-Lin Sheu, Yong Xia
This paper considers a fractional programming problem (P) which minimizes a ratio of quadratic functions subject to a two-sided quadratic constraint. As is well-known, the fraction…
On RIC bounds of Compressed Sensing Matrices for Approximating Sparse Solutions Using Quasi Norms
Yong Hsia, Ruey-Lin Sheu
This paper follows the recent discussion on the sparse solution recovery with quasi-norms when the sensing matrix possesses a Restricted Isometry Constant $δ_{2…
A Revisit to Quadratic Programming with One Inequality Quadratic Constraint via Matrix Pencil
Yong Hsia, Gang-Xuan Lin, Ruey-Lin Sheu
The quadratic programming over one inequality quadratic constraint (QP1QC) is a very special case of quadratically constrained quadratic programming (QCQP) and attracted much atten…
Trust Region Subproblem with a Fixed Number of Additional Linear Inequality Constraints has Polynomial Complexity
Yong Hsia, Ruey-Lin Sheu
The trust region subproblem with a fixed number m additional linear inequality constraints, denoted by (Tm), have drawn much attention recently. The question as to whether Problem…