From combinatorial optimization to real algebraic geometry and back by Janez Povh

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Formal proofs in real algebraic geometry: from ordered fields to quantifier elimination by Assia Mahboubi, Cyril Cohen

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Dualities in convex algebraic geometry by Philipp Rostalski, Bernd Sturmfels

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ON THE COMPLEXITY OF SEMIDEFINITE PROGRAMS ARISING IN POLYNOMIAL OPTIMIZATION by Igor Klep, Janez Povh, Angelika Wiegele

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An algebraic perspective on multivariate tight wavelet frames by Stöckler, Joachim., Charina, Maria., Putinar, Mihai., Scheiderer, Claus.

“…Recent advances in real algebraic geometry and in the theory of polynomial optimization are applied to answer some open questions in the theory of multivariate tight wavelet frames whose generators have at least one vanishing moment. …”
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Satisfiability of cross product terms is complete for real nondeterministic polytime Blum-Shub-Smale machines by Christian Herrmann, Johanna Sokoli, Martin Ziegler

“…Several problems, mostly from real algebraic geometry / polynomial systems, have been shown complete (under many-one reduction by polynomial-time Turing machines) for this class. …”
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Robust nonlinear stability and performance analysis of an F/A-18 aircraft model using sum of squares programming by Anderson, J, Papachristodoulou, A

“…The methods presented use the sum of squares decomposition and ideas from real algebraic geometry to represent polynomial non-negativity over closed sets to compute various system properties such as L2 gain, regions of attraction, reachable sets and nonlinear Hankel norm approximations. …”

Model validation and robust stability analysis of the bacterial heat shock response using SOSTOOLS by El-Samad, H, Prajna, S, Papachristodoulou, A, Khammash, M, Doyle, J, IEEE, IEEE

“…Combining ideas from robust control theory, real algebraic geometry, optimization and semidefinite programming, SOSTOOLS provides a promising framework to answer these robustness and model validation questions algorithmically. …”

A zero-dimensional approach to compute real radicals by Silke J. Spang

“…The notion of real radicals is a fundamental tool in Real Algebraic Geometry. It takes the role of the radical ideal in Complex Algebraic Geometry. …”
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The Non-Tightness of a Convex Relaxation to Rotation Recovery by Yuval Alfassi, Daniel Keren, Bruce Reznick

“…The methods we use are mostly drawn from the area of polynomial optimization and convex relaxation; we also use some results from real algebraic geometry, as well as Matlab optimization packages for PNP.…”
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Neural network verification using polynomial optimisation by Newton, M, Papachristodoulou, A

“…We approach the problem from a different perspective, using polynomial optimisation and real algebraic geometry (the Positivstellensatz) to assert the emptiness of a semi-algebraic set. …”

Spatial reasoning with augmented points: Extending cardinal directions with local distances by Reinhard Moratz, Jan Oliver Wallgrün

“…We provide a formal specification of EPRAm including a composition table for EPRA2 automatically determined using real algebraic geometry. We also report on an experimental performance analysis of EPRA2 in the context of a topological map-learning task proposed for benchmarking qualitative calculi. …”
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Coloured noise from stochastic inflows in reaction-diffusion systems by Adamer, M, Harrington, H, Gaffney, E, Woolley, T

“…To identify suitable models we use tools from real algebraic geometry that link the network structure to its dynamical properties. …”

Pell’s equation, sum-of-squares and equilibrium measures on a compact set by Lasserre, Jean B.

“…Interestingly, this view point connects orthogonal polynomials, Christoffel functions and equilibrium measures on one side, with sum-of-squares, convex optimization and certificates of positivity in real algebraic geometry on another side.…”
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Sparse polynomial optimisation for neural network verification by Newton, M, Papachristodoulou, A

“…We approach the problem from a different perspective, using sparse polynomial optimisation theory and Positivstellensatz, a key result in real algebraic geometry. The former exploits the natural cascading structure of the neural network using ideas from chordal sparsity while the latter tests the emptiness of a semi-algebraic set using algebra, to provide tight bounds. …”