62 citations · 104 across the 27 of their papers we have counts for
7 papers · 1 filter
Comment on "Approximation algorithms for quadratic programming"
Tongli Zhang, Yong Xia
The radius of the outer Dikin ellipsoid of the intersection of ellipsoids due to Fu et al. (J. Comb. Optim., 2, 29-50, 1998) is corrected from to . The approx…
On local minimizers of generalized trust-region subproblem
Jiulin Wang, Mengmeng Song, Yong Xia
Generalized trust-region subproblem (GT) is a nonconvex quadratic optimization with a single quadratic constraint. It reduces to the classical trust-region subproblem (T) if the co…
Local Optimality Conditions for a Class of Hidden Convex Optimization
Mengmeng Song, Yong Xia, Hongying Liu
Hidden convex optimization is such a class of nonconvex optimization problems that can be globally solved in polynomial time via equivalent convex programming reformulations. In th…
Unifying Farkas lemma and S-lemma: new theory and applications in nonquadratic nonconvex optimization
Meijia Yang, Yong Xia, Shu Wang
We unify nonlinear Farkas lemma and S-lemma to a generalized alternative theorem for nonlinear nonconvex system. It provides fruitful applications in globally solving nonconvex non…
Polyak's convexity theorem, Yuan's lemma and S-lemma: extensions and applications
Mengmeng Song, Yong Xia
We extend Polyak's theorem on the convexity of joint numerical range from three to any number of quadratic forms on condition that they can be generated by three quadratic forms wi…
Trust-region and -regularized subproblems: local nonglobal minimum is the second smallest objective function value among all first-order stationary points
Jiulin Wang, Mengmeng Song, Yong Xia
The local nonglobal minimizer of trust-region subproblem, if it exists, is shown to have the second smallest objective function value among all KKT points. This new property is ext…