The Linear Programming Solver
- Overview
- Getting Started
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Syntax
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Details
Presolve Pricing Strategies for the Primal and Dual Simplex Solvers The Network Simplex Algorithm The Interior Point Algorithm Macro Variable OROPTMODEL Iteration Log for the Primal and Dual Simplex Solvers Iteration Log for the Network Simplex Solver Iteration Log for the Interior Point Solver Problem Statistics Data Magnitude and Variable Bounds Variable and Constraint Status Irreducible Infeasible Set
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Examples
Diet Problem Reoptimizing the Diet Problem Using BASIS=WARMSTART Two-Person Zero-Sum Game Finding an Irreducible Infeasible Set Using the Network Simplex Solver Migration to OPTMODEL: Generalized Networks Migration to OPTMODEL: Maximum Flow Migration to OPTMODEL: Production, Inventory, Distribution Migration to OPTMODEL: Shortest Path
- References
| Macro Variable _OROPTMODEL_ |
The OPTMODEL procedure always creates and initializes a SAS macro called _OROPTMODEL_. This variable contains a character string. After each PROC OROPTMODEL run, you can examine this macro by specifying %put &_OROPTMODEL_; and check the execution of the most recently invoked solver from the value of the macro variable. The various terms of the variable after the LP solver is called are interpreted as follows.
- STATUS
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indicates the solver status at termination. It can take one of the following values:
- OK
The solver terminated normally.
- SYNTAX_ERROR
Incorrect syntax was used.
- DATA_ERROR
The input data were inconsistent.
- OUT_OF_MEMORY
Insufficient memory was allocated to the procedure.
- IO_ERROR
A problem occurred in reading or writing data.
- SEMANTIC_ERROR
An evaluation error, such as an invalid operand type, occurred.
- ERROR
The status cannot be classified into any of the preceding categories.
- SOLUTION_STATUS
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indicates the solution status at termination. It can take one of the following values:
- OPTIMAL
The solution is optimal.
- CONDITIONAL_OPTIMAL
The solution is optimal, but some infeasibilities (primal, dual or bound) exceed tolerances due to scaling or preprocessing.
- INFEASIBLE
The problem is infeasible.
- UNBOUNDED
The problem is unbounded.
- INFEASIBLE_OR_UNBOUNDED
The problem is infeasible or unbounded.
- BAD_PROBLEM_TYPE
The problem type is unsupported by the solver.
- ITERATION_LIMIT_REACHED
The maximum allowable number of iterations was reached.
- TIME_LIMIT_REACHED
The solver reached its execution time limit.
- FUNCTION_CALL_LIMIT_REACHED
The solver reached its limit on function evaluations.
- FAILED
The solver failed to converge, possibly due to numerical issues.
When SOLUTION_STATUS has a value of OPTIMAL, CONDITIONAL_OPTIMAL, ITERATION_LIMIT_REACHED, or TIME_LIMIT_REACHED, all terms of the _OROPTMODEL_ macro variable are present; for other values of SOLUTION_STATUS, some terms do not appear.
- OBJECTIVE
indicates the objective value obtained by the solver at termination.
- PRIMAL_INFEASIBILITY
indicates, for the primal simplex and dual simplex solvers, the maximum (absolute) violation of the primal constraints by the primal solution. For the interior point solver, this term indicates the relative violation of the primal constraints by the primal solution.
- DUAL_INFEASIBILITY
indicates, for the primal simplex and dual simplex solvers, the maximum (absolute) violation of the dual constraints by the dual solution. For the interior point solver, this term indicates the relative violation of the dual constraints by the dual solution.
- BOUND_INFEASIBILITY
indicates, for the primal simplex and dual simplex solvers, the maximum (absolute) violation of the lower or upper bounds by the primal solution. For the interior point solver, this term indicates the relative violation of the lower or upper bounds by the primal solution.
- DUALITY_GAP
indicates the (relative) duality gap. This term appears only if the option SOLVER= ITERATIVE is specified in the SOLVE statement.
- COMPLEMENTARITY
indicates the (absolute) complementarity. This term appears only if the option SOLVER= ITERATIVE is specified in the SOLVE statement.
- ITERATIONS
indicates the number of iterations taken to solve the problem. When the network simplex solver is used, this term indicates the number of network simplex iterations taken to solve the network relaxation. When crossover is enabled, this term indicates the number of interior point iterations taken to solve the problem.
- ITERATIONS2
indicates the number of simplex iterations performed by the secondary solver. The network simplex solver selects the secondary solver automatically unless a value has been specified for the SOLVER2= option. When crossover is enabled, the secondary solver is selected automatically. This term appears only if the network simplex solver is used or if crossover is enabled.
- PRESOLVE_TIME
indicates the time (in seconds) used in preprocessing.
- SOLUTION_TIME
indicates the time (in seconds) taken to solve the problem, including preprocessing time.
When SOLUTION_STATUS has a value of OPTIMAL, CONDITIONAL_OPTIMAL, ITERATION_LIMIT_REACHED, or TIME_LIMIT_REACHED, all terms of the _OROPTMODEL_ macro variable are present; for other values of SOLUTION_STATUS, some terms do not appear.