Elements of Convex Optimization Theory

This is a revised and extended version of Appendix A of Skiadas (2009), providing a self-contained overview of elements of convex optimization theory. The presentation is limited to the finite-dimensional case, but from an advanced perspective that is amenable to generalization. Some results, like the projection theorem and the Riesz representation theorem for Hilbert spaces, are stated and proved in a way that also applies to infinitedimensional spaces, since doing so comes at negligible additional cost. On the other hand, instances where the finite dimensionality assumption is essential are noted.