proxax

Certified first-order proximal point methods for unconstrained and constrained nonconvex composite optimization in JAX and Optax.

Documentation: https://proxax.readthedocs.io/

Installation

pip install proxax

Or with uv:

uv add proxax

Problem Classes

1. Unconstrained Nonconvex Composite Optimization: $$\min_{x \in \mathcal{X}} ; f(x) + h(x)$$ where $f$ (smooth) is differentiable and $(m, L^+)$-weakly convex/smooth on an arbitrary JAX PyTree $\mathcal{X}$, and $h$ (proximal) is proper, closed, convex, and proximable.

2. Set / Cone-Constrained Nonconvex Composite Optimization: $$\min_{x \in \mathcal{X}} ; f(x) + h(x) \quad \text{s.t.} \quad \mathcal{A}(x) \in \mathcal{C}$$ where $\mathcal{A}: \mathcal{X} \to \mathcal{Y}$ is a linear map between PyTrees and $\mathcal{C} \subseteq \mathcal{Y}$ is a closed convex set with Euclidean projection $\Pi_{\mathcal{C}}$.

Quick Example

import jax.numpy as jnp
import proxax
from proxax import constraints
from proxax import prox
from proxax import solvers

problem = proxax.CompositeProblem(
    smooth=lambda x: 0.5 * jnp.dot(x, q_mat @ x) + jnp.dot(c_vec, x),
    proximal=prox.Box(lower=-1.0, upper=1.0),
    constraints=constraints.equality(lambda x: a_mat @ x, rhs=b_vec),
)

sol = proxax.solve(problem, x0, solver=solvers.QPAIPP(opt_tol=1e-5, feas_tol=1e-5))

Available Certified Solvers (wwkong/nc_opt Suite)

• Unconstrained Composite (CompositeProblem): AIPP, APD (PF.APD), ECG, AG, UPFAG, NCFISTA, AdapFISTA, ACACG, AdapAPG
• Unconstrained Spectral (SpectralProblem / NuclearNorm): IAICG, DAICG
• Set / Cone-Constrained (CompositeProblem with constraints): QPAIPP, QPAPD, IALM (NL-IAPIAL / AIDAL), SProxALM, IAIPAL
• Optax Single-Step Transforms (proxax.optax_compat): proximal, aipp, apd, qp_aipp, qp_apd, ialm