Protocol Documentation

Constant function like `f(x_1, x_2) = 2`

Linear function like `f(x_1, x_2) = 2 x_1 + 3 x_2`

Quadratic function like `f(x_1, x_2) = 4 x_1 x_2 + 5 x_2`

Polynomial like `f(x_1, x_2) = 4 x_1^2 + 5 x_2^3 + 6 x_1 x_2^2 + 7 x_2^2 + 8 x_1 x_2 + 9 x_1 + 10 x_2 + 11`

Constraint ID - Constraint IDs are managed separately from decision variable IDs. We can use the same ID for both. For example, we have a decision variable `x` with decision variable ID `1`` and constraint `x == 0` with constraint ID `1`. - IDs are not required to be sequential. - IDs must be unique with other types of constraints.

Integer parameters of the constraint. Consider for example a problem constains a series of constraints `x[i, j] + y[i, j] <= 10` for `i = 1, 2, 3` and `j = 4, 5`, then 6 = 3x2 `Constraint` messages should be created corresponding to each pair of `i` and `j`. The `name` field of this message is intended to be a human-readable name of `x[i, j] + y[i, j] <= 10`, and the `subscripts` field is intended to be the value of `[i, j]` like `[1, 5]`.

Key-value parameters of the constraint.

Name of the constraint.

Detail human-readable description of the constraint.

The value of function for the state

IDs of decision variables used to evalute this constraint

Integer parameters of the constraint.

Key-value parameters of the constraint.

Name of the constraint.

Detail human-readable description of the constraint.

Value for the Lagrangian dual variable of this constraint. This is optional because not all solvers support to evaluate dual variables.

Lower bound of the decision variable.

Upper bound of the decision variable.

Decision variable ID. - IDs are not required to be sequential.

Kind of the decision variable

Bound of the decision variable If the bound is not specified, the decision variable is considered as unbounded.

Name of the decision variable. e.g. `x`

Subscripts of the decision variable. e.g. `[1, 3]` for an element of multidimensional deicion variable `x[1, 3]`

Additional parameters for decision variables

Detail human-readable description of the decision variable.

Decision variables used in this instance - This must constain every decision variables used in the objective and constraints. - This can contains a decision variable that is not used in the objective or constraints.

Constraints of the optimization problem

The sense of this problem, i.e. minimize the objective or maximize it. Design decision note: - This is a required field. Most mathematical modeling tools allow for an empty sense and default to minimization. Alternatively, some tools do not create such a field and represent maximization problems by negating the objective function. This project prefers explicit descriptions over implicit ones to avoid such ambiguity and to make it unnecessary for developers to look up the reference for the treatment of omitted cases.

The application or library name that created this message.

Error information by the solver which cannot be expressed by other messages. This string should be human-readable.

Some feasible or infeasible solution for the problem is found. Most of heuristic solvers should use this value.

The solver proved that the problem is infeasible, i.e. all solutions of the problem are infeasible. If the solver cannot get the proof of infeasibility, and just cannot find any feasible solution due to the time limit or due to heuristic algorithm limitation, the solver should return its *best* `Solution` message with `feasible` field set to `false`.

The solver proved that the problem is unbounded.

Whether the solution is feasible. Note that this is the feasiblity of the solution, not the problem. If the problem is infeasible, i.e. when the solver proves that all solution of the problem are infeasible, `Infeasible` message should be used.

The optimality of the solution.

Whether the solution is obtained by a relaxed linear programming solver.

The value of the solution for each variable ID.