Playing with Duality: An Overview of Recent Primal-Dual Approaches for Solving Large-Scale Optimization Problems

Understand

Optimization methods are at the core of many problems in signal/image processing, computer vision, and machine learning.

• For a long time, it has been recognized that looking at the dual of an optimization problem may drastically simplify its solution.
• Deriving efficient strategies which jointly brings into play the primal and the dual problems is however a more recent idea which has generated many important new contributions in the last years.
• These novel developments are grounded on recent advances in convex analysis, discrete optimization, parallel processing, and non-smooth optimization with emphasis on sparsity issues.