Invex optimization revisited

Ksenia Bestuzheva () and Hassan Hijazi ()
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Ksenia Bestuzheva: The Australian National University, Data61, CSIRO
Hassan Hijazi: The Australian National University, Data61, CSIRO

Journal of Global Optimization, 2019, vol. 74, issue 4, No 8, 753-782

Abstract: Abstract Given a non-convex optimization problem, we study conditions under which every Karush–Kuhn–Tucker (KKT) point is a global optimizer. This property is known as KT-invexity and allows to identify the subset of problems where an interior point method always converges to a global optimizer. In this work, we provide necessary conditions for KT-invexity in n dimensions and show that these conditions become sufficient in the two-dimensional case. As an application of our results, we study the Optimal Power Flow problem, showing that under mild assumptions on the variables’ bounds, our new necessary and sufficient conditions are met for problems with two degrees of freedom.

Keywords: Convex optimization; Invex optimization; Boundary-invexity; Optimal power flow (search for similar items in EconPapers)
Date: 2019
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DOI: 10.1007/s10898-018-0650-1

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