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Invex Optimization Revisited

Ksenia Bestuzheva(u5647146***at***anu.edu.au)
Hassan Hijazi(hassan.hijazi***at***anu.edu.au)

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 variable's bounds, our new necessary and sufficient conditions are met for problems with two degrees of freedom.

Keywords: Global Optimization, Invex Optimization, Convex Optimization, Optimal Power Flow

Category 1: Global Optimization (Theory )

Category 2: Nonlinear Optimization

Category 3: Applications -- Science and Engineering

Citation:

Download: [PDF]

Entry Submitted: 07/05/2017
Entry Accepted: 07/06/2017
Entry Last Modified: 07/05/2017

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