Numerical Algebraic Geometry and Optimization

摘要

Convex programming aims to minimize a convex objective function over a convex set, called the feasible set. For example, linear programming minimizes a linear function over a polytope (intersection of finitely many linear halfspaces as in Figure 1(a)) while semidefinite programming minimizes a linear function over a spectrahedron (intersection of the cone of positive semidefinite matrices with a linear space as in Figure 1(b)).