What are some good algorithms (and what are their run-times) for maximizing a convex function (let's say it's continuously differentiable, if that makes it any easier) within multiple linear constraints?

for example, an objective fnc f(x1, x2, x3, x4....), and constraints are x1 + 2x2 + x4 < const1, x3 < const2, etc.

Thanks in advance!

This post was edited by Kronosaurus on Jan 11 2014 10:10am

I've looked into this some more and am wondering whether the fact that the restrictions are always linear would make this problem easier to solve than typical nonlinear programming (I don't know much about nonlinear programming). Also, are there certain types of convex objective functions which are easier to solve?

Sorry about double post, won't let me edit :(

This post was edited by Kronosaurus on Jan 11 2014 10:40am

I would guess Lagrange multipliers would be the best way, but I'm not 100% sure what you are really asking.

What part needs clarification? Lagrange multipliers would work, but I'm asking for the most efficient programmatic solution pretty much.

a relevant read: https://www.ipam.ucla.edu/publications/optut/optut_9300.pdf