solution_summary should report multiple solutions

[odow]

It'd be helpful if solution_summary gave the number of solutions, as well as their statuses. This would have helped diagnose https://discourse.julialang.org/t/mosek-does-not-give-the-optimal-value-derived-by-simplex-methods/90727

[odow]

I played around locally, but this didn't seem to be an improvement:

julia> solution_summary(model)
* Solver : Gurobi

* Status
  Result count       : 20
  Termination status : OPTIMAL
  Solution #1
    Primal status    : FEASIBLE_POINT
    Dual status      : NO_SOLUTION
  Solution #2
    Primal status    : FEASIBLE_POINT
    Dual status      : NO_SOLUTION
  Solution #3
    Primal status    : FEASIBLE_POINT
    Dual status      : NO_SOLUTION
  Solution #4
    Primal status    : FEASIBLE_POINT
    Dual status      : NO_SOLUTION
  Solution #5
    Primal status    : FEASIBLE_POINT
    Dual status      : NO_SOLUTION
  Solution #6
    Primal status    : FEASIBLE_POINT
    Dual status      : NO_SOLUTION
  Solution #7
    Primal status    : FEASIBLE_POINT
    Dual status      : NO_SOLUTION
  Solution #8
    Primal status    : FEASIBLE_POINT
    Dual status      : NO_SOLUTION
  Solution #9
    Primal status    : FEASIBLE_POINT
    Dual status      : NO_SOLUTION
  Solution #10
    Primal status    : FEASIBLE_POINT
    Dual status      : NO_SOLUTION
  Solution #11
    Primal status    : FEASIBLE_POINT
    Dual status      : NO_SOLUTION
  Solution #12
    Primal status    : FEASIBLE_POINT
    Dual status      : NO_SOLUTION
  Solution #13
    Primal status    : FEASIBLE_POINT
    Dual status      : NO_SOLUTION
  Solution #14
    Primal status    : FEASIBLE_POINT
    Dual status      : NO_SOLUTION
  Solution #15
    Primal status    : FEASIBLE_POINT
    Dual status      : NO_SOLUTION
  Solution #16
    Primal status    : FEASIBLE_POINT
    Dual status      : NO_SOLUTION
  Solution #17
    Primal status    : FEASIBLE_POINT
    Dual status      : NO_SOLUTION
  Solution #18
    Primal status    : FEASIBLE_POINT
    Dual status      : NO_SOLUTION
  Solution #19
    Primal status    : FEASIBLE_POINT
    Dual status      : NO_SOLUTION
  Solution #20
    Primal status    : FEASIBLE_POINT
    Dual status      : NO_SOLUTION
  Message from the solver:
  "Model was solved to optimality (subject to tolerances), and an optimal solution is available."

* Candidate solution
  Objective value      : 0.00000e+00
  Objective bound      : 0.00000e+00
  Relative gap         : 0.00000e+00
  Dual objective value : 0.00000e+00

* Work counters
  Solve time (sec)   : 6.40609e-01
  Barrier iterations : 0
  Node count         : 11391

And the default case of

julia> solution_summary(model)
* Solver : HiGHS

* Status
  Result count       : 1
  Termination status : OPTIMAL
  Solution #1 (default)
    Primal status    : FEASIBLE_POINT
    Dual status      : FEASIBLE_POINT
  Message from the solver:
  "kHighsModelStatusOptimal"

just adds noise.

The discourse problem is really a bug in Mosek.jl.

[blegat]

Maybe make it a bit more visible that we are truncating solutions:

julia> solution_summary(model)
* Solver : HiGHS

* Status
  Result count       : 20
  Termination status : OPTIMAL
  Solution #1/20 (default)
    Primal status    : FEASIBLE_POINT
    Dual status      : FEASIBLE_POINT
  (other 19 solutions truncated for brevity, display them with `show_all_solutions=true`...)
  Message from the solver:
  "kHighsModelStatusOptimal"