53 citations · 273 across the 39 of their papers we have counts for
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Algebraic Degrees of Generalized Nash Equilibrium Problems
Jiawang Nie, Kristian Ranestad, Xindong Tang
This paper studies the algebraic degree of generalized Nash equilibrium problems (GNEPs) given by polynomials. Their generalized Nash equilibria (GNEs), as well as their KKT or Fri…
Quartic Spectrahedra
John Christian Ottem, Kristian Ranestad, Bernd Sturmfels +1
Quartic spectrahedra in 3-space form a semialgebraic set of dimension 24. This set is stratified by the location of its ten nodes. There are twenty maximal strata, identified recen…
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…
The Algebraic Degree of Semidefinite Programming
Jiawang Nie, Kristian Ranestad, Bernd Sturmfels
Given a generic semidefinite program, specified by matrices with rational entries, each coordinate of its optimal solution is an algebraic number. We study the degree of the minima…