spacecore-optimize

Optimization on top of SpaceCore. SpaceCore supplies spaces, geometry, operators, functionals and proximal steps; this package hands them to external optimizers and adds a catalogue of common objectives.

The one rule it enforces: an optimizer that works on flat coordinates gets the gradient as the covector X.riesz(F.grad(x)), not the Riesz gradient F.grad(x). On a Euclidean space the two coincide; on a weighted or operator geometry only the covector is the derivative with respect to the coordinates SciPy and optax update.

Install

pip install spacecore-optimize            # SciPy adapters and functionals
pip install "spacecore-optimize[optax]"   # plus minimize_optax (JAX backend)

Requires Python 3.11+ and SpaceCore 0.5.0+.

Example

Least squares on a space with a weighted inner product:

import numpy as np
import spacecore as sc
import spacecore_optimize as spo

ctx = sc.Context(sc.NumpyOps(), dtype=np.float64)
X = sc.DenseCoordinateSpace((3,), ctx, geometry=sc.WeightedInnerProduct(ctx.asarray([1.0, 4.0, 9.0])))
Y = sc.DenseCoordinateSpace((5,), ctx)
rng = np.random.default_rng(0)
A = sc.DenseLinOp(ctx.asarray(rng.standard_normal((5, 3))), X, Y, ctx)
b = ctx.asarray(rng.standard_normal(5))

F = spo.least_squares(A, b)                 # 1/2 ||A x - b||^2
result = spo.minimize_scipy(F, X.zeros())   # scipy.optimize.minimize, L-BFGS-B
x = result.x_element                        # the minimizer, an element of X

What is in it

The norms covered by SpaceCore's own prox rules (LpNormFunctional, SquaredL2NormFunctional, L1NormFunctional) live in SpaceCore.

Documentation

Published at https://pavlo3p.github.io/spacecore-optimize/. To build locally:

pip install -e ".[docs]"
sphinx-build -W docs docs/_build/html

License

Apache-2.0.