A Dantzig-type Large Portfolio Optimization Model and Its Efficient Fitting Algorithm*

Given the cyclical nature of market volatility and the increasing complexity of global financial systems, developing effective strategies for large-scale portfolio optimization is of critical importance. In this work, we propose a novel Dantzig-type portfolio optimization (DPO) model designed to help investors navigate these challenges and optimize their portfolios effectively. The model separately incorporates l1 and folded concave penalties, enabling the direct estimation of optimal portfolio weights while enforcing the sum constraint and accommodating both long and short positions. We establish the desired theoretical properties under mild regularity conditions, and introduce efficient parallel computing algorithms based on asset-splitting. Through extensive simulation studies, we investigate the superior effectiveness and efficiency of the DPO model and proposed algorithms. Furthermore, we illustrate the usefulness of the model by applying it to U.S. stock market datasets, including the constituent stocks of both S&P 500 and Russell 2000 indices.