Basic Solver Usage

This example provides a simple introduction to using rlaopt solvers.

Simple Quadratic Problem

Let’s solve a simple quadratic optimization problem:

import torch
from rlaopt.expression import Variable, Constant
from rlaopt.atoms import SumSquares
from rlaopt.solvers import ProxGrad, ProxGradConfig

# Create a variable
x = Variable((5,), name='x')

# Build a simple objective: ||x - target||^2
target = torch.ones(5)
# target is data, not a variable
target_const = Constant(target)

objective = SumSquares(x - target_const)

# Solve
config = ProxGradConfig(eta=0.1, max_iters=100, tol=1e-6)
solver = ProxGrad(objective, config)
result = solver.solve()

print(f"Solution: {result.variable_values}")
print(f"Target: {target}")
print(f"Final error: {result.err}")
print(f"Distance to target: {torch.linalg.norm(result.variable_values.to_flat_tensor() - target)}")

This should find \(x = \text{target}\), minimizing the squared distance.