Lectures on Nonsmooth Optimization

Qinian Jin graduated from Anhui Normal University in China with a bachelor degree and obtained his PhD degree from the Department of Mathematics at Rutgers University, New Brunswick, USA. He then joined the Mathematical  Sciences Institute at Australian National University in 2011. His research was supported by Australian Research Council (ARC) and he was awarded the Future Fellowship from ARC. His research interest covers inverse problems, numerical analysis, optimization, partial differential equations, geometric analysis. In particular his recent research focuses on using nonsmooth optimization technique to design algorithms for solving ill-posed inverse problems. He has published about 70 papers on international journals.

• Preface.- Introduction.- Convex sets and convex functions.- Subgradient and mirror descent methods.- Proximal algorithms.- Karush-Kuhn-Tucker theory and Lagrangian duality.- ADMM: alternating direction method of multipliers.- Primal dual splitting algorithms.- Error bound conditions and linear convergence.- Optimization with Kurdyka- Lojasiewicz property.- Semismooth Newton methods.- Stochastic algorithms.- References.- Index.