Dec 11, 2018 · It's possible for a convex optimization problem to have an optimal solution but no KKT points. Constraint qualifications such as Slater's condition, LICQ, MFCQ, etc. are necessary to ensure that an optimal solution will satisfy the KKT conditions. For example, consider the problem $\min x_{2}$ subject to $(x_{1}-1)^{2}+x_{2}^{2} \leq 1$

Jun 7, 2020 · The Linear Independence Constraint Qualification is NOT always satisfied in linear optimization problems, in particular when the gradients (rows of coefficients) of the active constraints are not independent.

Dec 14, 2020 · There are other constraint qualifications besides LICQ that you might use that could be much easier to establish. For example, you could use linear programming to determine whether Slater's constraint qualification was satisfied.

Aug 25, 2022 · The linearly independent constraint qualification (LICQ) is said to hold at a point when the gradients of all the binding constraint functions at the point are linearly independent. My understanding is LICQ guarantees the Karush Kuhn Tucker (KKT) conditions are met at …

May 10, 2017 · LICQ and a some nitty-gritty questions I've been looking into linearly independent constraint qualification (LICQ) to to offer some additional regularity. For convex problems, LICQ ensures that

Jun 24, 2022 · Stack Exchange Network. Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.

Stack Exchange Network. Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.

Sep 7, 2018 · LICQ is not a necessary condition for optimality. It is a prerequisite that the KKT conditions are necessary for optimality. You might check other constraint qualifications (MFCQ, linearity, convexity + Slater point, etc).

Jul 2, 2015 · Do we really need the LICQ for a first-order necessary optimality condition? What's wrong with the following conclusion from the set of implications that I collected (all references taken from the book given above)?

Aug 27, 2021 · However the linear independence constraint qualification (LICQ) fails everywhere, so in principle the KKT approach cannot be used directly. I have seen multiple examples solved like this, and I don't understand why this is legitimate. It seems to me that the correct approach would be to reason as follows: