# Optimizing convex function in an online manner

I have a convex function of $n$ variables, $f(x_1,x_2,\dots,x_n)$ and need to find its minimizer. Are there algorithms that can retrieve the minimizer in an online fashion? i.e. solve for $x_1^{(opt)}$, $x_2^{(opt)}$ and so on in a sequential manner?

• I don't know how you could possibly hope to know the optimal value of $x_1$ without also knowing the corresponding values of $x_2,\dots,x_n$ -- you can't even evaluate the function without knowing all of the $x$'s. In any case, even if the problem statement is meaningful, I suspect you're going to need to edit the question to give us more context. There are many techniques for convex optimization, and what to pick depends on the nature of the function $f$ and how it is specified. How is $f$ provided? As an expression? In what mini-language? What properties does $f$ have? – D.W. May 28 '18 at 5:28
• Possibly relevant: en.wikipedia.org/wiki/Coordinate_descent – D.W. May 28 '18 at 5:29