The Base versions of each product include Primal and Dual Simplex algorithms for linear models and includes integer programming capabilities. We offer a few different options that extend the capabilities of the base versions. Whether or not you need an option depends upon the types of models that you wish to solve. If your models are linear (with or without integer restrictions) no options are required.
The Barrier option adds a Barrier/Interior Point solver. If you have a quadratic model (i.e., an model with a quadratic objective function and/or quadratic constraints with all other terms being linear) then the Barrier option will provide the best performance. Quadratic models can be solved with the general Nonlinear solver but it will generally take longer. The Barrier option can also be used to solve linear models with no integer restrictions. In some cases using the Barrier algorithm may be significantly faster that using the Primal and Dual Simplex algorithms available in the base versions. This is typically true on sparse models with more than 5,000 constraints or highly degenerate models.
The Nonlinear option can allow you to solve general nonlinear models to a local optimum using a Generalized Reduced Gradient (GRG) algorithm. If your models are nonlinear and convex (i.e., only one local optimum) then you can use the Nonlinear option to solve your models. However, many classes of nonlinear models are non-convex (i.e., have more than one local optimum). Using the Nonlinear option alone, the solver will stop at the first locally optimal solution it finds. Other local optimum may exist that are significantly better than the local optimum returned. For nonconvex models you may want to use the Nonlinear option in conjunction with the Global option.
The Global option provides two additional techniques for solving nonlinear models – a Global solver and a Multistart capability. Rather than stopping after the first local optimum is found, the Global solver will search until the global optimum is confirmed. When limited time makes searching for the global optimum prohibitive, the Multistart capability can be a powerful tool for finding good solutions more quickly. This capability intelligently selects different starting points and solves each to a local optimum and then returns the best solution found. For non-convex nonlinear models, the quality of the solution returned using the Multistart capability will be superior to that of the general nonlinear solver. The Global option requires the Nonlinear option.