 The APOPT solver is freely available for commercial or academic purposes. The online version is the latest version with the most recent developments. APOPT Solver for AMPL and Pyomo APOPT Solver for APMonitor (MATLAB) APOPT Solver for APMonitor (Python) APOPT Solver for APMonitor (Julia) APOPT Solver for GEKKO (Python)

The APOPT solver has a number of options that are available for tuning the solver performance. Some of the available options and default values are listed below:

• minlp_maximum_iterations 10000 - maximum number of nlp solutions from the branch and bound method. A successful solution is returned if there is an integer solution upon reaching the maximum number of iterations. Otherwise, the solution is not considered to be successful and an error message is returned with the failed solution.
• minlp_max_iter_with_int_sol 500 - maximum number of nlp solutions when a candidate integer solution is found
• minlp_as_nlp 1 - solve minlp problem as a continuous nlp problem, ignoring integer constraints
• minlp_branch_method 3 - 1=depth first (find integer solution faster), 2=breadth first, 3=lowest objective leaf, 4=highest objective leaf
• minlp_gap_tol 1.0e-2 - gap is the spread between the lowest candidate leaf (obj_r=non-integer solution) and the best integer solution (obj_i). When the gap is below the minlp_gap_tol, the best integer solution is returned. The gap is defined as gap=(obj_i-obj_r)/max((abs(obj_i)+abs(obj_r))/2,1).
• minlp_integer_tol 1.0e-2 - amount that a candidate solution variable can deviate from an integer solution and still be considered an integer.
• minlp_integer_max 2.0e9 - maximum value to be considered as an integer. Values over 2147483647 or below -2147483648 not stored correctly with an internal integer variable type because of the number of bits used to store an integer.
• minlp_integer_leaves 1 - add additional integer leaves, 0=off, 1=integer leaves with inequality on branching, 2=integer leaves with equality constraint on branching.
• minlp_print_level 1 - print level (0-10). Development version has additional advanced diagnostics.
• nlp_maximum_iterations 500 - maximum number of iterations for each nlp sub-problem. Reducing the nlp maximum iterations can improve the solution speed because less computational time is spent on candidate solutions that may not converge
• objective_convergence_tolerance 1.0e-6 - convergence tolerance for the objective function. Values lower than 1.0e-10 sometimes run into covergence problems because of numerical scaling and cannot achieve the requested accuracy.
• constraint_convergence_tolerance 1.0e-6 - convergence tolerance for the constraints. A lower convergence tolerance typically adds only a couple additional iterations to the solution but the solution also does not change significantly.

Additional options are available for tuning of the solver performance and are included in the documentation.