Implementation of column generation

[angelafq]

This PR adds support for Column Generation (CG) and Dual Stabilized Column Generation (DCG) as hub algorithms in mpi-sppy, and introduces the PHSpoke class, addressing issue #617

Features:

• CG Hub: Implements Dantzig–Wolfe decomposition for scenario-based models. Iteratively builds a restricted master problem (RMP), solves for dual prices, broadcasts duals, and generates new columns by solving scenario subproblems.
• DCG Hub: Adds a stabilized variant by solving the dual of the master problem (dRMP) with a quadratic regularization term around a reference dual value (“bundle center”). Bundle center updates when the lower bound improves, reducing dual variable oscillations and improving convergence.
• PHSpoke: Implements a Progressive Hedging (PH) spoke, enabling communication of feasible solutions to CG based hubs.

New Classes:

• CGBase (in cgbase.py): Base class for column generation algorithms.
• CG (in cg.py): Implements the standard column generation algorithm.
• DCG (in dualcg.py): Implements the dual stabilized column generation algorithm.
• PHSpoke (in ph_spoke.py): Implements the Progressive Hedging spoke.

Integration with existing spokes is supported.

[Copilot]

Pull request overview

Adds Column Generation (CG) and Dual Stabilized Column Generation (DCG) as hub algorithms in mpi-sppy, plus a new PHSpoke and new spoke→hub data channel for feasible solutions.

Changes:

• Introduces new optimizers: CG, DCG, and shared base CGBase, plus new hub types CGHub/DCGHub.
• Adds a new spoke (PHSpoke) and a new SPWindow field (XFEAS) to transmit feasible solutions/costs from spokes to hubs.
• Wires new CLI/config options and vanilla cylinder constructors for CG/DCG hubs and PH spoke integration.

Reviewed changes

Copilot reviewed 11 out of 11 changed files in this pull request and generated 14 comments.

Show a summary per file

File	Description
mpisppy/utils/config.py	Adds config sections/options for CG/DCG hubs and PH spoke.
mpisppy/utils/cfg_vanilla.py	Adds vanilla constructors for CG/DCG hubs and PH spoke; tweaks timed_mipgap gating.
mpisppy/generic_cylinders.py	Registers new args and plugs CG/DCG hubs + PH spoke into decomposition selection.
mpisppy/cgbase.py	Implements the core column generation base algorithm and RMP plumbing.
mpisppy/opt/cg.py	Adds the standard CG optimizer entrypoint.
mpisppy/opt/dualcg.py	Adds dual-stabilized CG optimizer and dual master model.
mpisppy/cylinders/hub.py	Adds CGHub/DCGHub and RECENT_XHATS circular buffer handling + XFEAS reception.
mpisppy/cylinders/spwindow.py	Adds new Field.XFEAS and field-length mapping.
mpisppy/cylinders/spcommunicator.py	Adds receivers for BEST_XHAT and XFEAS and a receiver for RECENT_XHATS lists.
mpisppy/cylinders/ph_spoke.py	Adds new PH-based spoke that sends feasible solutions to hubs.
mpisppy/cylinders/subgradient_bounder.py	Extends bound spoke to also send feasible solutions (XFEAS).

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[angelafq]

When using CG (or DualCG), a rho value is not necessarily required, so raising an error here would be too restrictive and could block valid configurations. That is why I changed this to a warning. A better long-term fix may be to make this check conditional on whether a PH-based hub or spoke is actually being used.

[angelafq]

When using CG (or DualCG), a rho value is not necessarily required, so raising an error here would be too restrictive and could block valid configurations. That is why I changed this to a warning. A better long-term fix may be to make this check conditional on whether a PH-based hub or spoke is actually being used.