Lecture 12 : KKT conditions
نویسندگان
چکیده
The Lagrange dual function is: g(u, v) = min x L(x, u, v) The corresponding dual problem is: maxu,v g(u, v) subject to u ≥ 0 The Lagrange dual function can be viewd as a pointwise maximization of some affine functions so it is always concave. The dual problem is always convex even if the primal problem is not convex. For any primal problem and dual problem, the weak duality always holds: f∗ ≥ g∗ When the Slater’s conditioin is satisfied, we have strong duality so f∗ = g∗. The dual problem sometime can be easier to solve compared with the primal problem and the primal solution can be constructed from the dual solution.
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