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Solvers We Sell

We offer a selection of the highest-quality solvers, interfaced to AMPL for full access to algorithms and options. For your convenience we provide licensing and support on the same terms as the AMPL software. Our price list includes all of these solvers in a range of configurations.

The choice of a solver is determined mainly by the kind of problem to be solved and the optimizing algorithms to be applied. Usually several solvers are applicable to the problems that derive from a particular application; as solver performance is highly application-dependent, a choice among solvers is best made by testing on representative examples. Our free trials of AMPL include all of these solvers.

Our solver lineup is summarized below, with links to more detailed descriptions. We categorize the solvers according to whether they are based on classical “linear” methods, classical “nonlinear” methods, or “global” methods that draw from various approaches.

Linear-quadratic solvers

These solvers all handle linear and convex quadratic optimization problems in both continuous and integer variables:

Individual solvers offer extensions to additional problem types. All incorporate fast primal simplex, dual simplex, and interior methods for linear programming together with sophisticated branch-and-cut and heuristic search approaches for pure-integer and mixed-integer problems. Options for parallel computation on multiple processors and cores are included. Solvers in this category are the most widely used for diverse applications throughout business, government, and research organizations.

Nonlinear solvers

The solvers in this category provide the most effective way of finding locally optimal solutions to problems involving smooth nonlinear functions (including ratios, polynomials, exponentials and logarithms, and trigonometric forms). They offer a variety of proven algorithms:

  • CONOPT (ARKI Consulting & Development) — multi-method architecture founded on reduced gradient
  • KNITRO (Ziena Optimization) — choice of interior-point and active-set methods, with support for integer variables and automatic multiple starts
  • LOQO (Princeton University) — interior-point method applied to a sequence of quadratic approximations
  • MINOS (Stanford University) — reduced gradient approach founded on a linear primal simplex method
  • SNOPT (Stanford University) — sequential quadratic approximation method

For a given problem class, one or more of these solver approaches will generally be found advantageous. Nonlinear solvers are used extensively in applications such as energy transmission and engineering design that have a physical component, and in advanced economic and financial modeling.

Global solvers

These solvers combine a variety of approaches to find globally optimal solutions among many locally optimal points. Each is designed to handle a specially chosen combination of nonconvex, nonsmooth, and discrete expressions in the objective and constraints. We offer a selection of the best solvers available in this category:

Since the problems addressed by these solvers are particularly difficult, proper choice of a suitable solver is essential. Using AMPL, it is easy to try several solver alternatives on the same model and data, to determine what works best for a given application.