Suppose I had a problem: Maximize $f(\bf{x}) $ subject to the contraints $g_i(\bf{x})< b$
Can I still use Lagrange multipliers? My text says that the constraints need to be equalities.
2026-03-27 06:08:22.1774591702
Can I use Lagrange Multipliers with inequality constraints?
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You do want $\le$, not $<$, otherwise there is likely to be no maximum. The generalization of Lagrange multipliers to allow inequality constraints is the Karush-Kuhn-Tucker conditions.