The problem is constrained by a set of inequalities in the form of $$ \| A_i\mathbf{x}\|\geq \mathbf{y_i^Tx} $$ where x is a n-vector of unknowns, $A_i$ are matrices and $y_i$ vectors. Is it possible to transform those constraints to Second-Order cone constraints and solve a SOCP or to solve the problem in a different way? Is the set described by those constraints a convex cone?
2026-02-23 06:54:26.1771829666
SOCP formulation: wrong inequality direction in constraints
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No, the inequality $\|A_ix\|\geq y_i^T x$ does not typically describe a convex set, except for those degenerate cases where it happens to describe a half-space. I suspect those cases are not useful for you!
It is not difficult to see why: its complement is the set described by $\|A_ix\|< y_i^T x$, which is a convex cone.
You will not be able to express a model involving these constraints as an SOCP.