Nonlinear Programming

Nonlinear programming (NLP) is the process of solving a system of equalities and inequalities, collectively termed constraints, over a set of unknown real variables, along with an objective function to be maximized or minimized, where some of the constraints or the objective function are nonlinear.

Nonlinear programming problems are in general more difficult to solve than linear programming problems, and often the solution found is only a local optimum. The solution methods for nonlinear programming models vary, which can result in different nonlinear solvers giving different local optima for the same problem.

Benefits of using AIMMS as Nonlinear Programming Software for Optimization

Besides the general benefits of using AIMMS, there is some specific functionality that makes AIMMS Nonlinear Programming Software excellent for modeling nonlinear programming problems.

• Efficient Pre Solvers: AIMMS is equipped with a nonlinear presolver. With a presolve, nonlinear problems can be solved faster and the solution can improve. The nonlinear programming solver may even find a feasible solution for problems declared infeasible without the presolve, and in other cases provide proof that it really is infeasible.
• Multi-Start Algorithm: Our Nonlinear Programming Software also comes with an open customizable multi-start algorithm which may increase the chance of finding a good final solution.
• Efficient Hessian Calculation: AIMMS contains an efficient implementation of Hessian calculation which can speed up the solution process of some nonlinear programming solvers.
• Find the right solver: As the performance of the various available nonlinear programming solvers depends heavily on the specific problem, AIMMS makes it very easy to find the best solver for your specific problem by supporting links to many solvers.

Nonlinear Programming solvers

Standard Nonlinear Programming Solvers

AIMMS supports the solvers CONOPT, SNOPT, MINOS, and KNITRO, to solve nonlinear programming models. AIMMS also supports the global Optimization (GO) solvers LGO and BARON, which can find global optima for a certain subset of nonlinear programming problems, while the other solvers only guarantee local optima.

Open Solver Interface

The AIMMS Open Solver Interface allows solver developers to link their own nonlinear programming solvers to AIMMS themselves.