A Markowitz optimizer: objective, constraints, the efficient frontier and the cost of constraints on the same portfolio model.
Markowitz portfolio optimization finds the portfolios with the highest expected return for each level of risk: the efficient frontier. This tool solves for the global minimum-variance portfolio, the maximum-Sharpe tangency portfolio and portfolios with a target return or volatility, and shows how weight constraints such as no short selling cost efficiency.
The frontier portfolio with the highest Sharpe ratio. The line from the risk-free rate to it is the steepest possible capital allocation line.
Limits such as no short selling shrink the set of allowed portfolios, so the constrained frontier lies on or below the unconstrained one. The gap is the cost of the constraint.