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DOE OSTI · 1851409

Trust-Region Newton-CG with Strong Second-Order Complexity Guarantees for Nonconvex Optimization

Curtis, Frank E.·Robinson, Daniel P. (ORCID:0000000302514227)·Royer, Clément W. (ORCID:0000000324522172)·Wright, Stephen J. (ORCID:0000000168157379)
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Curtis, Frank E., Robinson, Daniel P. (ORCID:0000000302514227), Royer, Clément W. (ORCID:0000000324522172), Wright, Stephen J. (ORCID:0000000168157379). 2021-01-01. Trust-Region Newton-CG with Strong Second-Order Complexity Guarantees for Nonconvex Optimization. https://doi.org/10.1137/19m130563x

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The global magnificent four theory is the homological version of a maximally supersymmetric $(8+1)$-dimensional gauge theory on a Calabi-Yau fourfold fibered over a circle. In the case of a toric fourfold we conjecture the formula for its twisted Witten index. String-theoretically we count the BPS states of a system of $D0$-$D2$-$D4$-$D6$-$D8$-branes on the Calabi-Yau fourfold in the presence of a large Neveu-Schwarz $B$-field. Mathematically, we develop the equivariant $K$-theoretic DT4 theory, by constructing the four-valent vertex with generic plane partition asymptotics. Physically, the vertex is a supersymmetric localization of a non-commutative gauge theory in $8+1$ dimensions.

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