adding example from pricing problem (from max)

[Transurgeon]

Description

Please include a short summary of the change.
IPOPT converges to the same optimal solution as max's CCP method, but quite a bit faster.
Issue link (if applicable):

Type of change

• New feature (backwards compatible)
• New feature (breaking API changes)
• Bug fix
• Other (Documentation, CI, ...)

Contribution checklist

• Add our license to new files.
• Check that your code adheres to our coding style.
• Write unittests.
• Run the unittests and check that they’re passing.
• Run the benchmarks to make sure your change doesn’t introduce a regression.

[github-actions]

Benchmarks that have improved:

   before           after         ratio
 [4f101cc3]       [81fa7cd0]

•     1.12±0s          932±0ms     0.83  gini_portfolio.Cajas.time_compile_problem
  

Benchmarks that have stayed the same:

   before           after         ratio
 [4f101cc3]       [81fa7cd0]
      1.38±0s          1.48±0s     1.07  matrix_stuffing.ParamConeMatrixStuffing.time_compile_problem
      566±0ms          588±0ms     1.04  simple_QP_benchmarks.ParametrizedQPBenchmark.time_compile_problem
      284±0ms          294±0ms     1.04  matrix_stuffing.ParamSmallMatrixStuffing.time_compile_problem
      524±0ms          535±0ms     1.02  semidefinite_programming.SemidefiniteProgramming.time_compile_problem
      232±0ms          237±0ms     1.02  gini_portfolio.Murray.time_compile_problem
      4.57±0s          4.64±0s     1.02  huber_regression.HuberRegression.time_compile_problem
      2.87±0s          2.91±0s     1.01  quantum_hilbert_matrix.QuantumHilbertMatrix.time_compile_problem
      2.33±0s          2.36±0s     1.01  simple_LP_benchmarks.SimpleFullyParametrizedLPBenchmark.time_compile_problem
      4.96±0s          5.03±0s     1.01  optimal_advertising.OptimalAdvertising.time_compile_problem
      242±0ms          244±0ms     1.01  high_dim_convex_plasticity.ConvexPlasticity.time_compile_problem
      11.4±0s          11.5±0s     1.01  simple_LP_benchmarks.SimpleLPBenchmark.time_compile_problem
      338±0ms          341±0ms     1.01  gini_portfolio.Yitzhaki.time_compile_problem
      1.10±0s          1.10±0s     1.00  finance.FactorCovarianceModel.time_compile_problem
      292±0ms          292±0ms     1.00  slow_pruning_1668_benchmark.SlowPruningBenchmark.time_compile_problem
      22.7±0s          22.7±0s     1.00  sdp_segfault_1132_benchmark.SDPSegfault1132Benchmark.time_compile_problem
      255±0ms          255±0ms     1.00  simple_QP_benchmarks.SimpleQPBenchmark.time_compile_problem
      1.86±0s          1.86±0s     1.00  simple_QP_benchmarks.UnconstrainedQP.time_compile_problem
      946±0ms          943±0ms     1.00  simple_LP_benchmarks.SimpleScalarParametrizedLPBenchmark.time_compile_problem
      13.0±0s          13.0±0s     1.00  finance.CVaRBenchmark.time_compile_problem
      1.70±0s          1.69±0s     0.99  tv_inpainting.TvInpainting.time_compile_problem
     44.7±0ms         44.3±0ms     0.99  matrix_stuffing.SmallMatrixStuffing.time_compile_problem
      5.19±0s          5.13±0s     0.99  svm_l1_regularization.SVMWithL1Regularization.time_compile_problem
      734±0ms          721±0ms     0.98  matrix_stuffing.ConeMatrixStuffingBench.time_compile_problem
      897±0ms          832±0ms     0.93  simple_QP_benchmarks.LeastSquares.time_compile_problem

[Transurgeon]

should we keep these changes so that we don't rely on cvxpy's grad functionality?

[Transurgeon]

closing this as we were able to "solve" max's problem. (although he found a faster implementation with a convex majorization strategy?).