54 citations · 155 across the 71 of their papers we have counts for
4 papers · 2 filters
First Order Conditions for Semidefinite Representations of Convex Sets Defined by Rational or Singular Polynomials
Jiawang Nie
A set is called semidefinite representable or semidefinite programming (SDP) representable if it can be represented as the projection of a higher dimensional set which is represent…
Matrix Cubes Parametrized by Eigenvalues
Jiawang Nie, Bernd Sturmfels
An elimination problem in semidefinite programming is solved by means of tensor algebra. It concerns families of matrix cube problems whose constraints are the minimum and maximum…
Structured Semidefinite Representation of Some Convex Sets
J. William Helton, Jiawang Nie
Linear matrix Inequalities (LMIs) have had a major impact on control but formulating a problem as an LMI is an art. Recently there is the beginnings of a theory of which problems a…
Algebraic Degree of Polynomial Optimization
Jiawang Nie, Kristian Ranestad
Consider the polynomial optimization problem whose objective and constraints are all described by multivariate polynomials. Under some genericity assumptions, %% on these polynomia…