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Polynomial optimisation in power systems at IBM Research

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In power systems, problems that model alternating-current transmission constraints are of a great and growing importance, but notoriously difficult due to their non-convexity. We have shown —a variety of hierarchies of convexifications, whose optima converge to the global optimum of the non-convex problem —custom first- and second-order methods for solving the convexifications, which are competitive with leading heuristics —methods for switching from solving the convexification using the first-order methods (with trivial per-iteration time and memory requirements, but poor rates of convergence) to any second-order methods on the non-convex problem (with local quadratic convergence) based on Smale’s work in algebraic geometry. This allows one to tackle large-scale instances in practice and to guarantee global convergence in theory. This summarises recent papers in IEEE T . Power Systems [31(1): 539–546], IEEE T . Smart Grid [8(6): 2988-2998], and Optimization Methods and Software [32(4): 849-871], which are joint work with Bissan Ghaddar, Alan Liddell, Jie Liu, Martin Mevissen, and Martin Takac.

This talk is part of the Optimisation and Numerical Analysis Seminars series.

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