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Apr 16, 2014 at 18:13 comment added Cristóbal Guzmán You can try for each iteration to find a most-violated inequality (this could work e.g. if $g_i$ are strictly convex), and adding that inequality to your constraints. I don't know whether this is theoretically efficient, but at least avoids the problem pointed out by Brian below.
Mar 26, 2013 at 7:20 vote accept George
Mar 25, 2013 at 16:01 vote accept George
Mar 26, 2013 at 7:19
Mar 24, 2013 at 4:16 answer added Brian Borchers timeline score: 1
Mar 24, 2013 at 1:17 comment added Suvrit How about the other simple approach: start with some feasible $x_0$. At each step thereafter ensure that $x_k$ lies in the sublevel set defined by $f(x_0)$. So at least no $x_k$ will run off to infinity (though I guess the initial sublevel set must be closed)...
Mar 23, 2013 at 21:42 history asked George CC BY-SA 3.0