Hidden Convexity in Partially Separable Optimization
CentER Working Paper Series No. 2011-070
25 Pages Posted: 15 Jun 2011
Date Written: June 10, 2011
The paper identifies classes of nonconvex optimization problems whose convex relaxations have optimal solutions which at the same time are global optimal solutions of the original nonconvex problems. Such a hidden convexity property was so far limited to quadratically constrained quadratic problems with one or two constraints. We extend it here to problems with some partial separable structure. Among other things, the new hidden convexity results open up the possibility to solve multi-stage robust optimization problems using certain nonlinear decision rules.
Keywords: convex relaxation of nonconvex problems, hidden convexity, partially separable functions, robust optimization
JEL Classification: C61
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