Convex optimization columbia

In Lecture 21, in order to understand the continuity of convex functions of the boundary of their domain, after establishing their continuity on the interior, we generalize the notion of continuity of a function to that of lower and upper semi- continuity

When the objective function is con- vex, convex optimization usually produces the global minimum (Lecture 23)

In less-friendly optimization problems, we sometimes have to resort to approximation methods using computer programs

The dimension of a convex set Cis the dimension of the affine hull of C

As we will soon see, an m-simplex is the convex hull of m+1 affinely independent points

Assume Sis an affine space of dimension n 1 in Rn, and V its associated linear space