Add comprehensive OBC algorithm documentation page #168

Copilot · 2025-10-19T17:20:10Z

Overview

This PR addresses the request to explain the algorithm behind the occasionally binding constraints (OBC) implementation on a separate documentation page. Previously, the documentation only showed practical usage examples without explaining the underlying algorithm.

Changes

Created a new comprehensive documentation page docs/src/how-to/obc_algorithm.md that explains:

Mathematical Formulation

How max/min operators in model equations are automatically transformed
Model augmentation with auxiliary variables and anticipated shocks
Shock propagation equations implementing a telescoping sum mechanism
The role of the activeᵒᵇᶜshocks parameter in enabling/disabling OBC enforcement

Optimization Algorithm

The page documents the constrained optimization problem solved at each time period:

minimize:    Σᵢ (ϵᵒᵇᶜ⁽ⁱ⁾)²
subject to:  constraint_violation(ϵᵒᵇᶜ⁽⁰⁾, ..., ϵᵒᵇᶜ⁽ᴴ⁾) ≤ 0

Details include:

Objective function: minimizing anticipated shock magnitudes
Constraint violation function over the forecast horizon
Numerical solver: NLopt SLSQP with specific tolerance settings
Gradient computation using automatic differentiation

Implementation Details

Workflow: 5-step process for enforcing OBC during simulation/IRF computation
Key parameters: max_obc_horizon (default 40) and ignore_obc flag
Computational considerations: Performance scaling, numerical stability best practices, and known limitations
Academic references: Citations to Cuba-Borda et al. (2019) and Andreasen et al. (2018)
Comparison: Brief overview comparing with piecewise linear, global solution, and extended path methods

Documentation Structure

The new page is positioned under How-to guides → Algorithm for occasionally binding constraints, right after the existing practical usage guide. This provides a natural progression:

First, learn how to use OBC features (existing obc.md)
Then, understand the algorithm internals (new obc_algorithm.md)

The pages cross-reference each other for easy navigation.

Benefits

Users can now understand the theoretical foundation of OBC in MacroModelling.jl
Researchers can evaluate whether the approach is suitable for their models
Developers can better understand the implementation for future contributions
The documentation clarifies technical details like anticipated shock sequences and optimization settings

Closes #[issue_number]

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Co-authored-by: thorek1 <[email protected]>

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Add OBC algorithm documentation page

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Clarify activeᵒᵇᶜshocks and [x] notation in documentation

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Copilot AI changed the title ~~[WIP] Add documentation for OBC algorithm implementation~~ Add comprehensive OBC algorithm documentation page Oct 19, 2025

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Add comprehensive OBC algorithm documentation page #168

Add comprehensive OBC algorithm documentation page #168

Copilot AI commented Oct 19, 2025 •

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Add comprehensive OBC algorithm documentation page #168

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Mathematical Formulation

Optimization Algorithm

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Copilot AI commented Oct 19, 2025 •

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