I'm now constructing the course of Convex Optimization with Applications to Image Processing, Computer Vision and Machine Learning.
Main Contents
First touch to convex optimization: what's convex optimization, why and how convex optimization is important
Another expressions: duality theory - ask the dual if you have troubles
Variational analysis: how to mathematically analyze a practical problem, what's the beauty of variations
Fast numerical solvers (I): how and why convex optimization leads to fast and reliable algorithms, how to achieve a better convergence rate in numerics
Fast numerical solvers (II): how and why multiplier theories help to improve numerical algorithms
Convex optimization to non-convex and integer optimization problems: what a challenge comes from practical problems, how can convex relaxation helps
Special practical topics: how to apply math in real problems, e.g. image denoising and restoration, image segmentation and labeling, machine learning
Convex Analysis and Optimization by Bertsekas
Nonlinear Programming by Bertsekas
Convex Optimization by Boyd and Vandenberghe
Lectures on modern convex optimization: analysis, algorithms, Engineering Applications by Ben-Tal and Nemirovskiĭ
Hopefully it works out and appears soon!