Projection Onto Convex Sets Approach to Solve Homogeneous Self Dual Model of Portfolio Optimization

A portfolio optimization problem is a convex optimization problem that involves a linear objective function with quadratic constraints. One method for solving portfolio optimization problems is to convert the QCLP (quadratically constrained linear programming) model into a homogeneous self-dual (HSD) model. The homogeneous self-dual (HSD) model is a combination of primal and dual problems from conic programming and is based on determining a point from the intersection of two convex sets, a convex cone and a subspace. The projection onto convex sets (POCS) and averaged projection can be employed to determine the solution of the HSD model. In this paper, POCS is applied to solve QCLP on portfolio optimization. The resulting solution is the convergence value of the sequence constructed in the POCS method. From the sequence constructed in the POCS methods, we can see whether the QCLP problem in portfolio optimization has a solution or not.