Add DRAKE_ASSERT statements to ensure programs being solved in parallel are actually threadsafe.

[cohnt]

This change is 

[cohnt]

We recently added a couple pieces of code where we solve mathematical programs in parallel, without actually asserting that they're thread-safe. This isn't a problem, since they are thread-safe, but if someone changes these programs down the line and inadvertently makes them not-thread-safe, it could lead to very confusing errors.

+@AlexandreAmice for feature review on this one?

[AlexandreAmice]

You want to put the asserts right before solve.

Reviewed 3 of 3 files at r1, all commit messages.
Reviewable status: 2 unresolved discussions, LGTM missing from assignee AlexandreAmice, needs platform reviewer assigned, needs at least two assigned reviewers

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geometry/optimization/convex_set.cc line 123 at r1 (raw file):

  for (int i = 0; i < ssize(progs); ++i) {
    ConstructEmptyBoundednessProgram(&(progs[i]), s);
    DRAKE_ASSERT(progs[i].IsThreadSafe());

No need for this one here. Only need to check before calling solve

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geometry/optimization/convex_set.cc line 161 at r1 (raw file):

    progs[thread_num].linear_costs()[0].evaluator()->update_coefficient_entry(
        dimension, maximize ? -1 : 1);
    solver_interfaces[thread_num]->Solve(progs[thread_num], std::nullopt,

Put the asserts before Solve

[cohnt]

Reviewable status: 2 unresolved discussions, LGTM missing from assignee AlexandreAmice, needs platform reviewer assigned, needs at least two assigned reviewers

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geometry/optimization/convex_set.cc line 123 at r1 (raw file):

Previously, AlexandreAmice (Alexandre Amice) wrote…

No need for this one here. Only need to check before calling solve

Done.

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geometry/optimization/convex_set.cc line 161 at r1 (raw file):

Previously, AlexandreAmice (Alexandre Amice) wrote…

Put the asserts before Solve

Done.

[AlexandreAmice]

Reviewed 1 of 1 files at r2.
Reviewable status: needs platform reviewer assigned, needs at least two assigned reviewers