102 citations · 200 across the 13 of their papers we have counts for
4 papers · 1 filter
An algebraic geometry approach to nonlinear parametric optimization in control
Ioannis A. Fotiou, Philipp Rostalski, Bernd Sturmfels +1
We present a method for nonlinear parametric optimization based on algebraic geometry. The problem to be studied, which arises in optimal control, is to minimize a polynomial funct…
Algebraic Recipes for Integer Programming
Bernd Sturmfels
Integer programming is concerned with solving linear systems of equations over the non-negative integers. The basic question is to find a solution which minimizes a given linear ob…
Computing the Integer Programming Gap
Serkan Hosten, Bernd Sturmfels
We determine the maximal gap between the optimal values of an integer program and its linear programming relaxation, where the matrix and cost function are fixed but the right hand…
Minimizing Polynomial Functions
Pablo A. Parrilo, Bernd Sturmfels
We compare algorithms for global optimization of polynomial functions in many variables. It is demonstrated that existing algebraic methods (Gröbner bases, resultants, homotopy met…