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arXiv · 1805.00591

A Primal-Dual Interior Point Method for a Novel Type-2 Second Order Cone Optimization Problem

Md Sarowar Morshed·Chrysafis Vogiatzis·Md. Noor-E-Alam
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Abstract

In this paper, we define a new, special second order cone as a type-$k$ second order cone. We focus on the case of $k=2$, which can be viewed as SOCO with an additional {\em complicating variable}. For this new problem, we develop the necessary prerequisites, based on previous work for traditional SOCO. We then develop a primal-dual interior point algorithm for solving a type-2 second order conic optimization (SOCO) problem, based on a family of kernel functions suitable for this type-2 SOCO. We finally derive the following iteration bound for our framework: \[\frac{L^γ}{θκγ} \left[2N ψ\left( \frac{\varrho \left(τ/4N\right)}{\sqrt{1-θ}}\right)\right]^γ\log \frac{3N}ε.\]

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Md Sarowar Morshed, Chrysafis Vogiatzis, Md. Noor-E-Alam. 2019-12-18. A Primal-Dual Interior Point Method for a Novel Type-2 Second Order Cone Optimization Problem. https://doi.org/10.1016/j.rico.2021.100042

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