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I'm currently working on an optimization problem with a linear objective with linear and nonlinear constraints, i'm facing difficulties reaching a good solution, so i was advised to move the nonlinear constraints to the objective function if possible, transforming the problem to a problem with a nonlinear objective and linear constraints.

My question is: is the a problem with nonlinear objective and linear constraints always favored over one with a linear objective and nonlinear constraints? and why?

Thank you.

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This depends on the kind of non-linearity, especially if these constraints are convex.

It is also possible to try to convert the non-linear constraints into a possibly exponential number of linear constraints. These can then be added during the solution process.

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