Mean - Variance Portfolio Optimisation

QP is the optimization of a quadratic function subject to linear equality and inequality constraints. It arises in multiple objective decision making where the departure of the actual decisions from their corresponding ideal, or bliss, value can be evaluated using a weighted quadratic norm as a measure of deviation. The formulation of mean-variance optimization of uncertain systems also leads to. QP An important application of mean-variance is in simple optimal portfolio problems where the constraints are linear and the objective function is quadratic (Markowitz, 1959). The decision maker has to reconcile the conflicting desires of maximizing expected portfolio return, represented by the linear term, and minimizing the portfolio risk, represented by the quadratic (variance) term, in the objective function. Sequential algorithms require the solution of subproblems to generate descent QP QP directions for general nonlinear optimization and minimax.