Quadratic Constraints and SOCP

Frontline Systems' optimizers solve quadratically constrained programming (QCP) and second order cone programming (SOCP) problems using these methods:

For an explanation of these types of problems, please see Optimization Problem Types - Quadratic Constraints and Conic Optimization.The standard Microsoft Excel Solver and the Premium Solver (and most other optimization software) do not offer built-in facilities for solving QCP or SOCP problems.

Interior Point or Newton-Barrier Method

The Premium Solver Platform includes an SOCP Barrier Solver that uses a primal-dual Interior Point method to solve LP, QP, QCP, and SOCP problems up to 2,000 decision variables with excellent performance.  It can compute the search direction on each iteration using power class or dual scaling methods, alone or with a predictor-corrector adjustment.

The MOSEK Solver uses a state-of-the-art implementation of an Interior Point or Newton-Barrier method, called the Homogeneous Self-Dual method, to solve LP, QP, QCP, and SOCP problems of unlimited size, subject to available time and memory.  It has been tested on SOCP problems of over 100,000 variables, more than any other Solver of its kind.

In both Solvers, LP, QP and QCP problems can be transformed automatically into SOCP problems.  The MOSEK Solver also includes a state-of-the-art Simplex method for LP problems.