Solver capabilities

Solver packages declare which models they support through ConstraintCapabilities:

ConstraintCapabilities(; linear_eq, nonlinear_eq, linear_ineq, nonlinear_ineq,
                       linear_sd, nonlinear_sd, box, continuous, binary,
                       integer, infinite_bounds)

The fields (each true, false or missing for "not declared") are:

• linear_eq / nonlinear_eq: linear / nonlinear equality constraints,
• linear_ineq / nonlinear_ineq: linear / nonlinear inequality constraints,
• linear_sd / nonlinear_sd: linear / nonlinear semidefinite constraints,
• box: finite variable bounds,
• continuous, binary, integer: continuous, binary (0/1) and integer (non-binary) variables,
• infinite_bounds: variables with infinite (unbounded) bounds.

Constraint linearity is detected exactly for JuMP-converted models (from the expression graphs) and via the structural Hessian for other models: a function is structurally linear exactly when its Hessian pattern is empty. Functions that cannot be traced are conservatively classified as nonlinear.

solver_capabilities queries a solver's declared capabilities, merge_capabilities combines capability declarations (for meta-algorithms that forward their sub-solvers' capabilities), and checksubproblem! validates a model against the capabilities of the selected solver before optimization.