Mosek parse PSD constraint on 2x2 matrices as RotatedLorentzCone.

[hongkai-dai]

This change is 

[hongkai-dai]

+@AlexandreAmice for feature review please, thanks!

Reviewable status: LGTM missing from assignee AlexandreAmice, needs platform reviewer assigned, needs at least two assigned reviewers, missing label for release notes (waiting on @hongkai-dai)

[AlexandreAmice]

Reviewed 6 of 6 files at r1, all commit messages.
Reviewable status: 5 unresolved discussions, LGTM missing from assignee AlexandreAmice, needs platform reviewer assigned, needs at least two assigned reviewers, missing label for release notes (waiting on @hongkai-dai)

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solvers/test/non_convex_optimization_util_test.cc line 74 at r1 (raw file):

      CompareMatrices(Q1, Q1_expected, 3E-5, MatrixCompareType::absolute));
  EXPECT_TRUE(
      CompareMatrices(Q2, Q2_expected, 3E-5, MatrixCompareType::absolute));

This change seems unrelated.

Code quote:

  EXPECT_TRUE(
      CompareMatrices(Q1, Q1_expected, 3E-5, MatrixCompareType::absolute));
  EXPECT_TRUE(
      CompareMatrices(Q2, Q2_expected, 3E-5, MatrixCompareType::absolute));

---

solvers/mosek_solver_internal.h line 620 at r1 (raw file):

        continue;
      }
    }

Won't this cause you to skip all the other psd constraints?

Could you add a comment that PositiveSemidefiniteConstraint is only treated as an affine expression in a cone if it is a 2x2 matrix. The other dual solutions are treated in SetVariableBoundsDualSolution

Code quote:

    if constexpr (std::is_same_v<C, PositiveSemidefiniteConstraint>) {
      if (binding.evaluator()->matrix_rows() != 2) {
        continue;
      }
    }

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solvers/test/mosek_solver_test.cc line 539 at r1 (raw file):

  MosekSolver solver;
  if (solver.available()) {
    TestTrivial2x2SDP(solver, 1E-5, /*check_dual=*/true, /*dual_tol=*/1E-8);

This change makes the psd constraint less accurate? That seems very odd to me.

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solvers/test/mosek_solver_internal_test.cc line 191 at r1 (raw file):

  EXPECT_FALSE(F_subi.empty());
  EXPECT_FALSE(F_subj.empty());
  EXPECT_FALSE(F_valij.empty());

I think that this no longer tests what we want it to test anymore. I would completely remove the 2x2 matrix from this test so that these can stay EXPECT_TRUE

Code quote:

  EXPECT_FALSE(F_subi.empty());
  EXPECT_FALSE(F_subj.empty());
  EXPECT_FALSE(F_valij.empty());

---

solvers/test/mosek_solver_internal_test.cc line 205 at r1 (raw file):

  auto y = prog.NewContinuousVariables<4>();
  auto X1 = prog.NewSymmetricContinuousVariables<2>();
  auto X2 = prog.NewSymmetricContinuousVariables<3>();

I think here we likely want to add an X3 that is constrained to be in the PSD cone of size 3 or 4. Otherwise this test no longer tests the same thing.

Code quote:

auto X2 = prog.NewSymmetricContinuousVariables<3>();