The optimization problem that I am solving is of the form min ||x||^2 (square of l-2 norm of x) such that Mx <= b. Here x is a d-dimensional vector, M is the transpose of a d-dimensional vector and b is a scalar. I started this by writing the lagrangian for this which is 2x+(M^T)*lambda = 0, but after applying the complementary slackness condition, I am stuck and unable to solve this further.
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Use a Quadratic Programming solver. Or, don't square the norm in the objective function, and use an SOCP solver (many "QP" solvers also do SOCP). – Mark L. Stone Oct 20 '23 at 12:03
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Please see this Quick beginner guide for asking a well-received question – Lucky Chouhan Oct 20 '23 at 13:18