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Invex optimization revisited

Author

Listed:
  • Ksenia Bestuzheva

    (The Australian National University, Data61, CSIRO)

  • Hassan Hijazi

    (The Australian National University, Data61, CSIRO
    Los Alamos National Laboratory)

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.

Suggested Citation

  • Ksenia Bestuzheva & Hassan Hijazi, 2019. "Invex optimization revisited," Journal of Global Optimization, Springer, vol. 74(4), pages 753-782, August.
    • Handle: RePEc:spr:jglopt:v:74:y:2019:i:4:d:10.1007_s10898-018-0650-1
    DOI: 10.1007/s10898-018-0650-1
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