4 papers
Positivstellensätze for polynomial matrices with universal quantifiers
Feng Guo, Jie Wang
This paper investigates Positivstellensätze for polynomial matrices subject to universally quantified polynomial matrix inequality constraints. We first establish a matrix-valued…
Non-SOS Positivstellensätze for semi-algebraic sets defined by polynomial matrix inequalities
Feng Guo
This paper establishes new Positivstellensätze for polynomials that are positive on sets defined by polynomial matrix inequalities (PMIs). We extend the classical Handelman and Kr…
Sparse Polynomial Matrix Optimization
Jared Miller, Jie Wang, Feng Guo
A polynomial matrix inequality is a formula asserting that a polynomial matrix is positive semidefinite. Polynomial matrix optimization concerns minimizing the smallest eigenvalue…
Exploiting Sign Symmetries in Minimizing Sums of Rational Functions
Feng Guo, Jie Wang, Jianhao Zheng
This paper is devoted to the problem of minimizing a sum of rational functions over a basic semialgebraic set. We provide a hierarchy of sum of squares (SOS) relaxations that is du…