If you don't study for a doctorate or do theoretical research, it seems that convex analysis is basically unnecessary; Stay in the academic circle for two or three years and take the initiative to understand this field. The names of these masters will appear repeatedly in papers and references, so it is necessary to read their monographs ... Of course, many Daniel only write papers and have no time to write monographs. At this time, they should read newspapers well. ..

Convex analysis and convex optimization.

R.t. Rockefeller. Convex analysis. Princeton, 1970.

Boyd south and l Vandenberg. Convex optimization. Cambridge, 2004.

There is also a China scholar Paul Tseng (unfortunately) among the masters in the field of optimization.

Add a few books that I have been in general contact with:

Dimitri Betsikas. Convex analysis and optimization (convex optimization algorithm).