# Non-convex optimization theory as math discipline [closed]

From my point of view sometimes cost function can be non-convex.

Is it exist non-convex optimization as math theory direction as convex-optimization or is this task unsolveable?

What books/courses can you recomend?

Thanks

• Answer for own questions after some time - such mathematical area in strict sense doesnt' exist at all. "All non-covnex optimization is combination of art and heuristics and some other stuff" - S.Boyd, EE364B ( L11, 35:35 youtu.be/upMWYV7S1Y0?t=2140) Commented Nov 17, 2017 at 5:55

Non-convex optimization is as broad a subject as convex optimization so a book would only cover some parts and you'd definitely need to go further if you want to really have a big picture of the field.

That being said, I really like: Nonlinear and Mixed-Integer Optimization: Fundamentals and Applications from C.Floudas.

• Ok, thanks. I'm computer science guy. Relative to math courses in university - we try to localise convex parts and perform convex optimization in this places....But is non-convex optimization problem is solvable via some algorithms? (maybe with some general assumption) which doesn't need human task understanding or reformulation original non-convex problem to convex problem? Commented Feb 29, 2016 at 15:05
• As I know - We(humans) don't know how to solve graph automorphism effectively, without factorial complexity...And this task sounds simpler then non-convex optimization. Thanks for reference to the book, I will be glad to any resources -- because for me it sounds like a magic. Commented Feb 29, 2016 at 15:12
• I get skills in convex optimization and I liked it. I did it through S.Boyd book, I watched his courses EE364A/EE364B in youtube and attend in his course EE364A as remtoe student. I planed to read Boris Polyak book and look his lectures. Commented Nov 17, 2017 at 5:59