*Handle*- Handle to a solver state
*Cost*- Value of returned solution

A solver that was setup manually with lp_solve/2 needs to be triggered explicitly using this predicate.

The external solver's LP, QP or MIP solver is applied to the problem represented by Handle. Precisely which method is used depends on the options given to lp_setup/4. lp_solve/2 fails if there is no solution or succeeds if an optimal solution is found, returning the solution's cost in Cost (unlike with lp_demon_setup/5, Cost gets instantiated to a number). After a success, various solution and status information can be retrieved using lp_get/3 and lp_var_get/4.

Normally, the external solver is invoked once per call in this predicate, but if the problem contain cutpool constraints (see lp_add_cutpool_constraints/4), then the external solver may be invoked repeatedly to produce a solution which does not violate the cutpool constraints.

When a solver is triggered repeatedly, each invocation will automatically take into account the current variable bounds. The set of constraints considered by the solver is the one given when the solver was created plus any new constraints that were added (lp_add/3) in the meantime.

The user can define their own handlers (per eplex instance/problem) to handle cases where there was some error condition, or some limits were exceeded during the solving of the problem. If no handler was defined, by default an event would be raised. These are:

- suboptimal handler (eplex_suboptimal event)
- This means that a solution was found but it may be suboptimal. The default behaviour is to print a warning and succeed.
- unbounded_handler (eplex_unbounded event)
- This means that the problem is unbounded. The default behaviour is to bind Cost to infinity (positive or negative depending on the optimisation direction), print a warning and succeed. CAUTION: No solution values are computed when the problem is unbounded, so unless the problem was set up with the solution(no) option, an error will occur when trying to continue as if the optimisation had succeeded.
- infeasible_handler (eplex_infeasible event)
- This means that the problem is infeasible. The default behaviour is to fail. Redefining this handler allows the examination of the failed problem, e.g. obtaining an IIS for it.
- unknown_handler (eplex_unknown event)
- This means that due to the solution method chosen, it is unknown whether the problem is unbounded or infeasible. The default behaviour is to print a warning and fail (even though this may be logically wrong!).
- abort_handler (eplex_abort event)
- Some other error condition occurred during optimisation. The default behaviour is to print an error and abort.

*(eplex_suboptimal)*- Solution was found, but is possibly suboptimal
*(eplex_unbounded)*- Problem is unbounded, no solution values
*(eplex_unknown)*- Result is unknown (infeasible or unbounded)
*(eplex_abort)*- External solver aborted for some reason
*(40) stale object handle*- Handle not valid: solver state had been destroyed by cleanup