DrawDown constraints and portfolio optimization

The seminal work by Markowitz in 1959 introduced portfolio theory to the world. The prevailing notion since then has been that portfolio risk is non linear i.e. you cannot use Linear Programming (LP) to optimize your portfolio. We will in this paper show that simple portfolio drawdown constraints are indeed linear and can be used to find for example maximum risk adjusted return portfolios. VaR for these portfolios can then be estimated directly instead of using computer intensive Monte Carlo methods.