We will consider convex optimization problems that can be formulated by using, in some combination, second-order cones, cones of symmetric positive semidefinite matrices, power functions and $p$-norms, entropy function, certain multivariate polynomial inequalities, convex exponential functions, nuclear norm and many others. We will review some of the progress on solving such problems by algorithms derived via self-concordant functions.

The most recent results to be reported are based on joint work with Mehdi Karimi.