Module robust 

Robust Optimization and Distributionally Robust Optimization

This module provides robust optimization methods that hedge against uncertainty in problem data. These algorithms are essential for risk-aware decision making under uncertainty.

Uncertainty Models

• Box uncertainty: Each parameter perturbed independently within ±δ
• Ellipsoidal uncertainty: Parameters perturbed inside an ellipsoid defined by a covariance matrix
• Polyhedral uncertainty: Parameters perturbed within a polytope (Aξ ≤ b)
• Budgeted uncertainty: Bertsimas-Sim model with total budget Γ

Algorithms

• box_robust: Worst-case evaluation over box uncertainty set
• ellipsoidal_robust: Worst-case evaluation over ellipsoidal uncertainty set
• distributionally_robust_cvar: CVaR-based distributionally robust objective
• saa_solve: Sample Average Approximation (Kleywegt-Shapiro-Homem-de-Mello)

Sub-modules

• minimax: Minimax optimization (subgradient, bundle, Nesterov smoothing, fictitious play)
• robust_lp: Robust linear programming (box, ellipsoidal, budgeted uncertainty)
• worst_case: Worst-case analysis, AARC, scenario approach, Wasserstein DRO

References

• Ben-Tal, A., El Ghaoui, L., & Nemirovski, A. (2009). Robust Optimization.
• Bertsimas, D. & Sim, M. (2004). “The price of robustness”. Operations Research.
• Shapiro, A., Dentcheva, D., & Ruszczyński, A. (2014). Lectures on Stochastic Programming.

Modules

minimax

Minimax Optimization Methods for Robust Optimization

robust_lp

Robust Linear Programming

worst_case

Worst-Case Analysis and Scenario-Based Robust Optimization

Structs

RobustConfig

High-level configuration for robust optimization.

RobustProblem

Configuration for a robust optimization problem.

SaaConfig

Options for the SAA solver.

SaaResult

Result of a Sample Average Approximation solve.

Enums

UncertaintySet

Describes the geometry of an uncertainty set for robust optimization.

UncertaintyType

Type of uncertainty set used in robust optimization.

Functions

box_robust

Evaluate the worst-case objective over an axis-aligned box uncertainty set.

distributionally_robust_cvar

Distributionally robust CVaR (Conditional Value-at-Risk) objective.

ellipsoidal_robust

Evaluate the worst-case objective over an ellipsoidal uncertainty set.

saa_solve

Solve a stochastic program via Sample Average Approximation (SAA).