This repository contains code for solving nonconvex separable optimization problems of the form

$$ \begin{align} \text{minimize } \ &\sum_{i=1}^n f_i(x_i) \\ \text{subject to } \ &\sum_{i=1}^n A_i x_i \leq b \\ &x_i \in \text{dom}(f_i), \quad i=1, \dots, n \end{align} $$

where the functions $f_i$ and their domains need not be convex.

The full theoretical background can be found in our paper:

Benjamin Dubois-Taine, Laurent Pfeiffer, Nadia Oudjane, Adrien Seguret, Francis Bach. "Two-stage stochastic algorithm for solving large-scale (non)-convex separable optimization problems under affine constraints". In: arXiv preprint [arXiv link].

If your problem is convex, you should define the problem by creating a child of the ConvexSeparableOptProblem class defined in separable_opt_problem.py and implementing the required functions.

If your problem is nonconvex, you should define a child of the NonConvexSeparableOptProblem class defined in separable_opt_problem.py and implementing the required functions. You can use the file PEVs/pev_problem.py as template.

You can then run the two-stage solver implemented in two_stage_solver.py

To reproduce the experiment from the first plot on the charging of electric vehicles problem, run the following in PEVs folder:

$ python script.py

To reproduce the experiment from the second plot on the charging of electric vehicles problem, run the following in PEVs folder:

$ python script_nonconvex.py

You can use the jupyter notebook to reproduce the plots.

To cite our work please use:

@article{dubois2026two,
  title={Two-stage stochastic algorithm for solving large-scale (non)-convex separable optimization problems under affine constraints},
  author={Dubois-Taine, Benjamin and Pfeiffer, Laurent and Oudjane, Nadia and Seguret, Adrien and Bach, Francis},
  journal={arXiv preprint arXiv:2602.06637},
  year={2026}
}