Add Deflation methods

[dpanici]

Deflation method motivation: find multiple solutions to non-convex optimization problems (which can include certain equilibirum solves)

This PR adds a couple ways to apply deflation methods in stellarator optimization and equilibrium solving

• adds a new equilibrium objective ForceBalanceDeflated which is the usual force balance, but multiplied by the deflation operator M(x;y) = 1/(x-y)^p + sigma
• adds a new generic objective DeflationOperator whose cost is simply M(x;y) = 1/(x-y)^p + sigma (to add as constraints to an optimization like in Tarek 2022 work)

References:

• Riley 2024 - for the "exp" deflation type
• Farrell 2015 - for the addition of the shift parameter and the general form of deflation used

TODO

• add tests
• update changelog
• update ForceBalanceDeflated to use pytree inputs for params_to_deflate_with
• add option for using single shift, like discussed in Riley 2024

Future work for another PR:

• Implement algorithms from Riley 2024
  • Implement deflated line-search Gauss-Newton algorithm like they use
  • Adapt their algorithm for our usual trust-region approach
• Add a wrapper objective so that one can multiply the deflation operator with any arbitrary objective, instead of only able to add it as an extra cost when doing stage one/two optimization.

[github-actions]

Memory benchmark result

|               Test Name                |      %Δ      |    Master (MB)     |      PR (MB)       |    Δ (MB)    |    Time PR (s)     |  Time Master (s)   |
| -------------------------------------- | ------------ | ------------------ | ------------------ | ------------ | ------------------ | ------------------ |
  test_objective_jac_w7x                 |    2.68 %    |     3.934e+03      |     4.039e+03      |    105.25    |       41.60        |       38.47        |
  test_proximal_jac_w7x_with_eq_update   |    1.07 %    |     6.547e+03      |     6.617e+03      |    70.20     |       179.88       |       179.09       |
  test_proximal_freeb_jac                |    0.11 %    |     1.322e+04      |     1.324e+04      |    14.39     |       93.87        |       92.87        |
  test_proximal_freeb_jac_blocked        |    0.00 %    |     7.543e+03      |     7.543e+03      |     0.29     |       82.94        |       82.23        |
  test_proximal_freeb_jac_batched        |   -0.17 %    |     7.529e+03      |     7.516e+03      |    -12.84    |       82.05        |       81.95        |
  test_proximal_jac_ripple               |    0.25 %    |     3.524e+03      |     3.533e+03      |     8.84     |       66.32        |       65.82        |
  test_proximal_jac_ripple_bounce1d      |   -0.58 %    |     3.715e+03      |     3.693e+03      |    -21.52    |       77.48        |       76.95        |
  test_eq_solve                          |   -0.04 %    |     1.991e+03      |     1.990e+03      |    -0.82     |       91.90        |       91.09        |

For the memory plots, go to the summary of Memory Benchmarks workflow and download the artifact.