1 citations · 1 across the 6 of their papers we have counts for
6 papers
The non-Archimedean Nirgendsnegativsemidefinitheitsstellensatz is not true
Hao Liang, Sizhuo Yan, Jianting Yang +1
Klep and Schweighofer asked whether the Nirgendsnegativsemide-finitheitsstellensatz holds for a symmetric noncommutative polynomial whose evaluations at bounded self-adjoint operat…
Lower Bounds of Functions on Finite Abelian Groups
Jiangting Yang, Ke Ye, Lihong Zhi
The problem of computing the optimum of a function on a finite set is an important problem in mathematics and computer science. Many combinatorial problems such as MAX-SAT and MAXC…
A Characterization of Perfect Strategies for Mirror Games
Sizhuo Yan, Jianting Yang, Tianshi Yu +1
We associate mirror games with the universal game algebra and use the *-representation to describe quantum commuting operator strategies. We provide an algebraic characterization o…
Extensions of S-Lemma for Noncommutative Polynomials
Feng Guo, Sizhuo Yan, Lihong Zhi
We consider the problem of extending the classical S-lemma from commutative case to noncommutative cases. We show that a symmetric quadratic homogeneous matrix-valued polynomial is…
Lifts of Non-compact Convex Sets and Cone Factorizations
Chu Wang, Lihong Zhi
In this paper we generalize the factorization theorem of Gouveia, Parrilo and Thomas to a broader class of convex sets. Given a general convex set, we define a slack operator assoc…
Certificates of Impossibility of Hilbert-Artin Representations of a Given Degree for Definite Polynomials and Functions
Feng Guo, Erich L. Kaltofen, Lihong Zhi
We deploy numerical semidefinite programming and conversion to exact rational inequalities to certify that for a positive semidefinite input polynomial or rational function, any re…