33 lines
1004 B
Python
33 lines
1004 B
Python
from __future__ import annotations
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import numpy as np
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def admm_lite(A: np.ndarray, b: np.ndarray, rho: float = 1.0, max_iter: int = 50, tol: float = 1e-4):
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"""Very lightweight ADMM solver for a toy problem: minimize 0.5||Ax - b||^2 + regularization.
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Returns the primal variable x. This is a minimal placeholder to demonstrate the schema.
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"""
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m, n = A.shape
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x = np.zeros(n)
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z = np.zeros(n)
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u = np.zeros(n)
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for _ in range(max_iter):
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# x-update (least-squares step)
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q = A.T @ b
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x = np.linalg.solve(A.T @ A + rho * np.eye(n), q + rho * (z - u))
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# z-update (soft-threshold for L1-like regularization placeholder)
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z_old = z.copy()
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z = _soft_threshold(x + u, rho)
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# u-update
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u += x - z
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# Convergence check
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if np.linalg.norm(z - z_old) < tol:
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break
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return x
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def _soft_threshold(v: np.ndarray, lam: float) -> np.ndarray:
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return np.sign(v) * np.maximum(np.abs(v) - lam, 0.0)
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