Create an N-Dimensional Power Cone Constraint

Constrains \((W, z)\) to lie in the N-dimensional power cone: $$\prod W_i^{\alpha_i} \ge |z|, \quad W \ge 0$$ where \(\alpha_i > 0\) and \(\sum \alpha_i = 1\).

Usage

PowConeND(W, z, alpha, axis = 2L, constr_id = NULL)

Arguments

W

A CVXR expression (vector or matrix).

z

A CVXR expression (scalar or vector).

alpha

A CVXR expression with positive entries summing to 1 along the specified axis.

axis

Integer, 2 (default, column-wise) or 1 (row-wise).

constr_id

Optional integer constraint ID.

Value

A PowConeND constraint object.

Known limitations

The R clarabel solver does not currently support the PowConeND cone specification. Problems involving PowConeND (e.g., exact geometric mean with more than 2 arguments) should use SCS or MOSEK as the solver, or use approximation-based atoms (e.g., geo_mean(x, approx = TRUE)).

See also

PowCone3D