Quadratic Programming Methods

In this document, we introduce three distinct methods for solving convex quadratic programming problems, each with unique advantages and specific application scenarios. First, we present the QuadLagR method. This approach utilizes the Lagrange method to handle equality constraints and has been extensively proven to deliver high-precision results. The implementation typically involves constructing a Lagrangian function and solving the resulting system of equations using matrix operations. If your problem contains equality constraints, QuadLagR may be your optimal choice. Second, we have the ActiveSet method. This technique employs the active set strategy to manage inequality constraints and demonstrates high efficiency when dealing with large-scale problems. The algorithm works by iteratively identifying active constraints and solving equality-constrained subproblems. If your problem involves numerous inequality constraints, ActiveSet could be your preferred solution. Finally, we introduce the TrackRoute method. This approach uses path following methodology to handle inequality constraints and excels in solving high-dimensional problems. The implementation follows a homotopy path from a starting point to the solution, maintaining feasibility throughout the process. For high-dimensional problems with substantial inequality constraints, TrackRoute may be your best option. We hope this information proves valuable for your work!