Supported atoms

BLVPY checks the lower source expression tree as well as CVXPY’s final cone program. An atom appearing in this table is necessary but not sufficient for model support; see also Structural requirements.

The table is exhaustive for source nodes that BLVPY audits directly. Real affine nodes are accepted as a class; every audited nonlinear node appears in its own row.

CVXPY syntax	Mathematical expression	Conic form
Any real affine expression	\(Ax+b\)	Affine
cp.abs(x)	\(|x|\)	LP
cp.cummax(x, axis=...)	\(\left(\max_{j\leq i}x_j\right)_i\)	LP
cp.dotsort(x, W)	\(\left\langle\operatorname{sort}(\operatorname{vec}x), \operatorname{sort}(\operatorname{vec}W)\right\rangle\)	LP
cp.entr(x)	\(-x\log x\) elementwise	EXP
cp.exp(x)	\(e^x\) elementwise	EXP
cp.geo_mean(x, p=..., approx=True)	\(\displaystyle\prod_i x_i^{w_i}\), where \(w=p/(\mathbf{1}^{\mathsf T}p)\)	SOC
cp.huber(x, M)	\(\begin{cases}x^2,&|x|\leq M,\\2M|x|-M^2,&|x|>M\end{cases}\)	SOC
cp.kl_div(x, y)	\(x\log(x/y)-x+y\) elementwise	EXP
cp.log(x)	\(\log x\) elementwise	EXP
cp.log1p(x)	\(\log(1+x)\) elementwise	EXP
cp.log_sum_exp(x, axis=..., keepdims=...)	\(\log\left(\sum_i e^{x_i}\right)\)	EXP
cp.logistic(x)	\(\log(1+e^x)\) elementwise	EXP
cp.max(x, axis=...)	\(\max_i x_i\)	LP
cp.maximum(x, y)	\(\left(\max\{x_i,y_i\}\right)_i\)	LP
cp.min(x, axis=...)	\(\min_i x_i\)	LP
cp.minimum(x, y)	\(\left(\min\{x_i,y_i\}\right)_i\)	LP
cp.norm1(x)	\(\displaystyle\sum_i |x_i|\)	LP
cp.norm_inf(x)	\(\displaystyle\max_i |x_i|\)	LP
cp.pnorm(x, p, approx=True)	\(\begin{cases}(\sum_i |x_i|^p)^{1/p},&p>1,\\ (\sum_i x_i^p)^{1/p},&p<1,\ x\geq0\end{cases}\)	SOC
cp.pnorm(x, p, approx=False)	\(\begin{cases}(\sum_i |x_i|^p)^{1/p},&p>1,\\ (\sum_i x_i^p)^{1/p},&p<1,\ x\geq0\end{cases}\)	LP / SOC / P3D
cp.power(x, p, approx=True)	\(x^p\) elementwise	SOC
cp.power(x, p, approx=False)	\(x^p\) elementwise	Affine / SOC / P3D
cp.quad_form(x, P)	\(x^TPx\)	SOC
cp.quad_over_lin(x, y)	\(\|x\|_2^2/y\)	SOC
cp.rel_entr(x, y)	\(x\log(x/y)\) elementwise	EXP
cp.sum_largest(x, k)	\(\displaystyle\sum_{i=1}^k x_{[i]}\)	LP
cp.xexp(x)	\(xe^x\) elementwise	EXP / SOC

Vector-valued expressions are flattened where needed. Sorting in dotsort uses the same order for both arguments, while \(x_{[i]}\) denotes the \(i\)th largest entry in sum_largest. Reduction indices follow the selected axis; abs, huber, and power act elementwise. The atom data \(W\), \(M\), \(p\), \(P\), and \(k\) must satisfy CVXPY’s usual constantness, domain, curvature, and DPP rules.

Exact rational representations

CVXPY’s approximate geometric-mean, p-norm, and power atoms use rational SOC representations. BLVPY accepts them only when CVXPY reports a finite approx_error exactly equal to zero. A tiny nonzero value is still an approximation and is rejected without a numerical tolerance.

Using approx=False for cp.power or cp.pnorm selects CVXPY’s exact representation, which uses 3D power cones for the general case and simpler cones for special exponents. BLVPY supports those forms. Direct scalar and vectorized cp.PowCone3D constraints are also supported. Exact cp.geo_mean and direct cp.PowConeND constraints produce generalized power cones and remain unsupported. Convenience wrappers that do not expose an approx argument keep their normal CVXPY representation.

Note that here the exactness describes the canonical graph representation, not the numerical cone-distance estimates; see Cone distance diagnostics.

Exponential representations

The listed exponential-family atoms use exact exponential-cone graphs. BLVPY also supports direct scalar, vector, and matrix cp.ExpCone constraints. Vector and matrix entries become three-row exponential-cone blocks in CVXPY’s canonical element order.

BLVPY audits exactness from the constructed expression graph. Convenience functions such as cp.loggamma and cp.log_normcdf return compositions of primitive atoms rather than distinct source nodes, so BLVPY evaluates those compositions according to their constituent atoms. Any approximation embodied in such a composition remains part of the modeled expression. Explicit quadrature constraints such as RelEntrConeQuad and OpRelEntrConeQuad remain unsupported.