cyclic coordinate descent

Asked Dec 27 '16 at 16:13

Active Dec 27 '16 at 16:13

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is it possible to implement cyclic coordinate descent to numerically solve optimization problem with equality constraints like: $$\mathrm{min} \quad f(x)$$ $$a^\top x=b$$ Suppose f(x): $\mathrm{R}^n\to \mathrm{R}$ convex and it is not hard to update $x_i$ when $x_j$, $j \neq i$ fixed, how to satisfy the equality constraint to achieve feasibility?

Thanks a lot!

asked Dec 27 '16 at 16:13

franjuncis

Maybe the problem is still easy after using $a^Tx=b$ to substitute out one variable. – LinAlg Dec 27 '16 at 19:07
thanks@LinAlg. um.. can you elaborate your idea a bit more? – franjuncis Dec 28 '16 at 05:42
If $a^Tx = b$ is $x_1 + 2x_2 + x_3 = 5$, you can write $x_1 = 5-2x_2-x_3$ to get rid of $x_1$ in the objective function. – LinAlg Dec 28 '16 at 09:29
Presumably that might negate the "ease" of the coordinate descent. Really curious about the context of the problem. – wonko Dec 28 '16 at 21:02

cyclic coordinate descent

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