Conditions for Exact Convex Relaxation and No Spurious Local Optima | IEEE Journals & Magazine | IEEE Xplore

Conditions for Exact Convex Relaxation and No Spurious Local Optima


Abstract:

Nonconvex optimization problems can be approximately solved via relaxation or local algorithms. For many practical problems such as optimal power flow (OPF) problems, bot...Show More

Abstract:

Nonconvex optimization problems can be approximately solved via relaxation or local algorithms. For many practical problems such as optimal power flow (OPF) problems, both approaches tend to succeed in the sense that relaxation is usually exact and local algorithms usually converge to a global optimum. In this article, we study conditions that are sufficient or necessary for such nonconvex problems to simultaneously have exact relaxation and no spurious local optima. These conditions help explain the widespread empirical experience that OPF problems, even though computationally hard in theory, seem to be easy in practice.
Published in: IEEE Transactions on Control of Network Systems ( Volume: 9, Issue: 3, September 2022)
Page(s): 1468 - 1480
Date of Publication: 16 September 2021

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