Robust feasibility of systems of quadratic equations using topological degree theory

نویسندگان

چکیده

We consider the problem of measuring margin robust feasibility solutions to a system nonlinear equations. study special case quadratic equations, which shows up in many practical applications such as power grid and other infrastructure networks. This is generalization quadratically constrained programming (QCQP), NP-Hard general setting. develop approaches based on topological degree theory estimate bounds robustness systems. Our methods use tools from convex analysis optimization cast problems checking conditions for problem. then inner bound outer procedures this problem, could be solved efficiently derive lower upper bounds, respectively, feasibility. evaluate our approach numerically standard instances taken MATPOWER NESTA databases AC flow equations that describe steady state grid. The results demonstrate can produce tight instances.

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ژورنال

عنوان ژورنال: Optimization Letters

سال: 2023

ISSN: ['1862-4480', '1862-4472']

DOI: https://doi.org/10.1007/s11590-023-02015-7