Robust & Constrained Optimization

Robust optimization stops pretending inputs are known: instead of a single expected-return vector, specify an uncertainty set around it and pick the portfolio with the best worst-case behavior inside the set, so the optimizer refuses positions that only look attractive because of input noise. Much of the benefit comes from better inputs rather than exotic sets: Ledoit–Wolf shrinkage blends the ill-conditioned sample covariance matrix toward a structured target, cutting estimation error sharply in high dimensions. Turnover penalties, norm constraints, and weight bounds serve the same end. The theme is humility: respect the noise in your estimates, so live weights resemble backtested ones.