Patent Document ID: 7593880
Application ID: 10390709
Patent Flag: 1

Claim One:
1. A method for determining optimal solutions along an efficient frontier comprising, a collection of security allocations for a portfolio by using a sequential linear programming technique for a problem having a nonlinear constraint, the method comprising: (a) generating a first optimal solution point along the efficient frontier by solving a relaxed linear programming problem with a plurality of linear constraints that excludes the nonlinear constraint using a processor of a computing device, the plurality of linear constraints forming a feasible region; (b) calculating a first tangent plane for the nonlinear constraint at said first optimal solution point using the processor of the computing device; (c) shifting the first tangent plane for the nonlinear constraint by a small step size to produce an additional linear constraint using the processor of the computing device, wherein the additional linear constraint lies within the feasible region; (d) generating a second optimal solution point along the efficient frontier by solving the relaxed linear programming problem with the additional linear constraint using the processor of the computing device; (e) calculating a second tangent plane for the nonlinear constraint at said second optimal solution point using the processor of the computing device; (f) shifting the second tangent plane for the nonlinear constraint by a small step size to produce a second additional linear constraint using the processor of the computing device, wherein the second additional linear constraint lies within the feasible region; and (g) generating additional optimal solution points along the efficient frontier by solving the relaxed linear programming problem with additional linear constraints using the processor of the computing device.