Stop hyphenating "symmetry breaking"

Numerical-optimization.md

@@ -27,11 +27,11 @@ Uniform regularization can be seen as an interpolation between Newton’s method
 
 _To be added_
 
-### Gratuitous symmetry-breaking
+### Gratuitous symmetry breaking
 
 In some cases, a configuration has a symmetry that must be broken to satisfy a newly imposed constraint. This happens, for example, when a point at the origin is constrained to lie on a sphere centered at the origin. In other cases, however, a configuration has a symmetry which is logically and aesthetically compatible with a newly imposed constraint. This happens, for example, when three equal-curvature spheres that intersect each other at 90° angles are constrained to instead intersect each other at 60° angles. A user might reasonably expect the realization process to preserve this symmetry, at least approximately. When it doesn’t, we’ll say the symmetry has been _gratuitously broken_.
 
-The idea of gratuitous symmetry-breaking can be extended to approximate symmetries. For example, suppose three spheres of roughly the same curvature intersect each other at roughly 90° angles. If we constrain these spheres to intersect each other at 60° angles, we might reasonably expect their curvatures to stay roughly the same as each other. If the curvatures instead come out wildly different from each other, we can say that the approximate symmetry of the initial configuration has been gratuitously broken.
+The idea of gratuitous symmetry breaking can be extended to approximate symmetries. For example, suppose three spheres of roughly the same curvature intersect each other at roughly 90° angles. If we constrain these spheres to intersect each other at 60° angles, we might reasonably expect their curvatures to stay roughly the same as each other. If the curvatures instead come out wildly different from each other, we can say that the approximate symmetry of the initial configuration has been gratuitously broken.
 
 ## Methods
 
@@ -105,7 +105,7 @@ When $f^{(2)}_p$ isn’t guaranteed to be positive-definite, we can use a modifi
 ```
 where the modification $E \in \operatorname{End}(V)$ is symmetric with respect to $(\_\!\_, \_\!\_)$ and balances some notion of smallness against the requirement that $\tilde{F}^{(2)}_p + E$ be safely positive-definite [CH, §1][NW, §3.4]. The hallmark of a modified Cholesky decomposition is that it directly produces a Cholesky decomposition of a pivoted version of $\tilde{F}^{(2)}_p + E$, with no need to produce $E$ as an intermediate step, and its speed is comparable to the ordinary Cholesky decomposition [CH, §1].
 
-The [`modcholesky`](https://argmin-rs.github.io/modcholesky/modcholesky/) crate implements the modified Cholesky decompositions from [GMW], [SE90], and [SE99]. In our application, they tend to exhibit [flightiness](#flightiness) and [gratuitous symmetry-breaking](#gratuitous-symmetry-breaking). The latter might be caused by pivoting, which differentiates between the elements of an arbitrary orthonormal basis in a way that isn’t directly related to the problem we’re trying to solve.
+The [`modcholesky`](https://argmin-rs.github.io/modcholesky/modcholesky/) crate implements the modified Cholesky decompositions from [GMW], [SE90], and [SE99]. In our application, they tend to exhibit [flightiness](#flightiness) and [gratuitous symmetry breaking](#gratuitous-symmetry-breaking). The latter might be caused by pivoting, which differentiates between the elements of an arbitrary orthonormal basis in a way that isn’t directly related to the problem we’re trying to solve.
 
 - **[CH]** Sheung Hun Cheng and Nicholas J. Higham. [“A Modified Cholesky Algorithm Based on a Symmetric Indefinite Factorization.”](https://doi.org/10.1137/S0895479896302898) _SIAM Journal on Matrix Analysis and Applications_ 19(4), 1998.
 - **[GMW]** Philip E. Gill, Walter Murray and Margaret H. Wright. [_Practical Optimization._](https://doi.org/10.1137/1.9781611975604) Academic Press, 1981.