How to get a feasible point of an arbitrary optimization model?

Specific Domains Optimization (Mathematical)
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1

How to get a feasible point if the optimization model is not infeasible?

If the model has no objective, I can do this by:

using JuMP, HiGHS
m = Model(HiGHS.Optimizer)
@variable(m, x <= 1)
optimize!(m)
value(x)

But if it do have an objective, this method will no longer work:

using JuMP, HiGHS
m = Model(HiGHS.Optimizer)
@variable(m, x <= 1)
@objective(m, Min, x)
optimize!(m)
value(x)

In other words, I am asking how to delete the objective from a model, or directly, is there any more concise syntax in JuMP to check the feasibility of an objective optimization model and get one of its feasible points when it exists?

Thanks!

2

Maybe just modify the objective to zero, check for feasibility, and reset the objective back?

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3

OK, thanks! :handshake: I thought there was more general approaches…

Thank you again!

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4

Just to clarify, the suggested approaches would be:

@objective(m, Min, 0.0)
optimize!(m)

or

set_objective_sense(m, MOI.FEASIBILITY_SENSE)
optimize!(m)
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5

Oh, thanks! I’ve got it. :handshake: :handshake:

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6

Hi, excuse me. May I ask how to obtain a different solution of a feasibility problem with JuMP after a feasible solution has been achived?

7

JuMP and solvers like HiGHS return a solution to the optimization problem that you formulate. If there are multiple solutions, there is no guarantee about which solution will be returned.

If you want to return a different solution, you must change the problem in some way. Either by adding a different objective, or by adding a new constraint that makes the previous solution infeasible.

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8

Could you further clarify “by adding a different objective”? If we target a problem with a meaning objective (rather than a feasiblity problem), is “by adding a new constraint that makes the previous solution infeasible” the only choice?

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9

If you just care about feasible solutions then the objective doesn’t matter.

If you want multiple optimal solutions to a MIP, see

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