Slater's Condition is a criterion used in optimization that ensures the existence of Lagrange multipliers for a convex optimization problem. Specifically, it states that if there exists at least one point in the interior of the feasible region that satisfies all inequality constraints strictly, then strong duality holds. This condition is important because it guarantees that the dual problem has the same optimal value as the primal problem, enhancing the understanding of dual cones and their applications in convex geometry.
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