4 citations · 5 across the 12 of their papers we have counts for
12 papers
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…
An SDP method for Fractional Semi-infinite Programming Problems with SOS-convex polynomials
Feng Guo, Meijun Zhang
In this paper, we study a class of fractional semi-infinite polynomial programming problems involving s.o.s-convex polynomial functions. For such a problem, by a conic reformulatio…
On Solving a Class of Fractional Semi-infinite Polynomial Programming Problems
Feng Guo, Liguo Jiao
In this paper, we study a class of fractional semi-infinite polynomial programming (FSIPP) problems, in which the objective is a fraction of a convex polynomial and a concave polyn…
On continuous selections of polynomial functions
Feng Guo, Liguo Jiao, Do Sang Kim
A continuous selection of polynomial functions is a continuous function whose domain can be partitioned into finitely many pieces on which the function coincides with a polynomial.…
On types of KKT points in polynomial optimization
Feng Guo, Do Sang Kim, Liguo Jiao +1
Let be a real polynomial function with variables and be a basic closed semialgebraic set in . In this paper, we are interested in the problem of identifying…
Global Łojasiewicz inequalities on comparing the rate of growth of polynomial functions
Si-Tiep Dinh, Feng Guo, Tien-Son Pham
We present a global version of the Łojasiewicz inequality on comparing the rate of growth of two polynomial functions in the case the mapping defined by these functions is (Newton)…
On semi-infinite systems of convex polynomial inequalities and polynomial
Feng Guo, Xiaoxia Sun
We consider the semi-infinite system of polynomial inequalities of the form \[ \mathbf{K}:=\{x\in\mathbb{R}^m\mid p(x,y)\ge 0,\ \ \forall y\in S\subseteq\mathbb{R}^n\}, \] where $p…
On types of degenerate critical points of real polynomial functions
Feng Guo, Tien-Son Pham
In this paper, we consider the problem of identifying the type (local minimizer, maximizer or saddle point) of a given isolated real critical point , which is degenerate, of a m…
Martingale Representation and Logarithmic-Sobolev Inequality for Fractional Ornstein-Uhlenbeck Measure
Xiaoxia Sun, Feng Guo
In this paper, we consider the measure determined by a fractional Ornstein-Uhlenbeck process. For such measure, we establish a martingale representation theorem and consequently ob…
Semidefinite programming relaxations for linear semi-infinite polynomial programming
Feng Guo, Xiaoxia Sun
This paper studies a class of so-called linear semi-infinite polynomial programming (LSIPP) problems. It is a subclass of linear semi-infinite programming problems whose constraint…
Semidefinite representations of non-compact convex sets
Feng Guo, Chu Wang, Lihong Zhi
We consider the problem of the semidefinite representation of a class of non-compact basic semialgebraic sets. We introduce the conditions of pointedness and closedness at infinity…
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…