Portfolio Optimization and the Successive Convex Approximation Framework

Abstract

Mean-variance Optimization (MVO) was a foundational, Nobel Prize-winning approach in portfolio optimization, introduced by Harry Markowitz in 1952 focusing on balancing risk and return. This talk explores the Successive Convex Approximation (SCA) Framework as a powerful method to address more complex and realistic portfolio optimization problems. In particular, we introduce theory involving convex geometry and optimization and the classic forms and types of constrained optimization problems in finance under the mean-variance framework. We then introduce non-convex optimization problems, in particular optimizing higher-order (MVSK) portfolios, and how the Majorization-Minimization method and SCA solve such non-convex problems iteratively (including a proof of the convergence of the MM algorithm).

Slides were updated on December 11, 2025.