Portfolio Optimization Models and MILANO

Below are two portfolio optimization models that incorporate discrete decisions: transaction costs, round-lot purchases, and sector constraints are considered in the first model and buy-in thresholds are added into the second model. Both models come with real-world data consisting of 20, 50, 100, 200, and 400 stocks from the S&P 500. The models are expressed in a form to be solved by MILANO.