PowConeND: Create an N-Dimensional Power Cone Constraint

In CVXR: Disciplined Convex Optimization

Create an N-Dimensional Power Cone Constraint

Description

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

CVXR documentation built on March 6, 2026, 9:10 a.m.