For a typical nonlinear problem,if you change the right-hand side by even a small amount,the dual value changes.

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In the context of optimization, the dual value (or shadow price) associated with a constraint reflects the rate at which the objective function's value changes as the right-hand side of the constraint is varied. For linear problems, this relationship is direct and the dual value remains constant for small changes in the right-hand side. For nonlinear problems, although the relationship between changes in the right-hand side and changes in the objective function might be more complex due to the nonlinearity, it is not accurate to say that for any typical nonlinear problem, a small change in the right-hand side will always result in a change in the dual value. The impact of such changes can vary significantly depending on the specific structure and properties of the nonlinear problem.

For a Typical Nonlinear Problem,if You Change the Right-Hand Side