A model, which defines a mathematical problem, and multiple directives may be received. Each of the multiple directives may be mapped to a respective linear solver instance. The linear solver instances may be launched to execute in parallel. Each of the linear solver instances may use either a primal or a dual algorithm and may further use double arithmetic, exact arithmetic, or hybrid arithmetic, as specified by corresponding ones of the multiple directives. A linear solver instance that uses hybrid arithmetic may start by using double arithmetic and may use exact arithmetic after experiencing a numerical difficulty. After the numerical difficulty is resolved, the linear solver instance that uses hybrid arithmetic may restart and continue to solve the mathematical problem using double arithmetic. After one of the linear solver instances finds an optimal solution, others of the linear solver instances may be stopped and a report may be provided.