.

asking for convex and non-convex is close to asking for everything !

.

anyway, when it comes to convex optimization and machine learning, i would recommend

Convex Optimization: Algorithms and Complexity

Sébastien Bubeck

https://arxiv.org/abs/1405.4980

.

regarding non-convex optimization, you might start here

https://www.microsoft.com/en-us/research/project/provable-non-convex-optimization-for-machine-learning-problems/

.

.

asking for convex and non-convex is close to asking for everything !

.

anyway, when it comes to convex optimization and machine learning, i would recommend

Convex Optimization: Algorithms and Complexity

Sébastien Bubeck

https://arxiv.org/abs/1405.4980

.

regarding non-convex optimization, you might start here

https://www.microsoft.com/en-us/research/project/provable-non-convex-optimization-for-machine-learning-problems/

.

An easy to read book on convex optimization can be found here

http://stanford.edu/~boyd/cvxbook/

A word of caution. Twenty years ago, individuals either wrote their own convex optimization for things like SVM or tried to find ones that were much faster than others.  Many individuals used the optimization algorithm from Orsuna's MIT CS thesis.  By 2001, it was clear that much more powerful, faster convex optimization algorithms were needed.

Specifically, my interest is focused on a probabilistic view of ML. 

For example, estimation of parameters in probability distributions using convex or nonconvex optimization....