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I have a Quadratically Constrained Linear Program that is supposed to be solved via KKT but I am interested to solve with simple Lagrange multiplier method by interchanging variables with little numerical tricks and get away the equations. Is this a useless effort and do we need KKT instead for such problem? Is Simple Lagrange solution applicable only to linear equality constraints? |
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Lagrange multipliers can only be used if your constraints are all equality constraints. If your constraints are inequality constraints you need KKT conditions on the dual variables corresponding to the inequality constraints. They are very similar to Lagrange conditions, however, with the addition of non-negativity of the dual variables and complementary slackness (but only if strong duality holds for your problem). Note though that if your quadratic constraints are equality constraints then your problem is nonconvex, and hence Lagrange multipliers will only give you necessary conditions for optimality, not sufficient conditions. |
