A Level-set Method For Convex Optimization with a Feasible Solution Path

Large-scale constrained convex optimization problems arise in several application domains. First-order methods are good candidates to tackle such problems due to their low iteration complexity and memory requirement. The level-set framework extends the applicability of first-order methods to tackle problems with complicated convex objectives and constraint sets. Current methods based on this framework either rely … Read more

An inexact proximal path-following algorithm for constrained convex minimization

Many scientific and engineering applications feature large-scale non-smooth convex minimization problems over convex sets. In this paper, we address an important instance of this broad class where we assume that the non-smooth objective is equipped with a tractable proximity operator and that the convex constraints afford a self-concordant barrier. We provide a new joint treatment … Read more