The Linear Programming Solver
- Overview
- Getting Started
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Syntax
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DetailsPresolvePricing Strategies for the Primal and Dual Simplex SolversThe Network Simplex AlgorithmThe Interior Point AlgorithmIteration Log for the Primal and Dual Simplex SolversIteration Log for the Network Simplex SolverIteration Log for the Interior Point SolverIteration Log for the Crossover AlgorithmConcurrent LPProblem StatisticsVariable and Constraint StatusIrreducible Infeasible SetMacro Variable _OROPTMODEL_
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ExamplesDiet ProblemReoptimizing the Diet Problem Using BASIS=WARMSTARTTwo-Person Zero-Sum GameFinding an Irreducible Infeasible SetUsing the Network Simplex SolverMigration to OPTMODEL: Generalized NetworksMigration to OPTMODEL: Maximum FlowMigration to OPTMODEL: Production, Inventory, DistributionMigration to OPTMODEL: Shortest Path
- References
The crossover algorithm takes an optimal solution from the interior point solver and transforms it into an optimal basic solution. The iterations of the crossover algorithm are similar to simplex iterations; this similarity is reflected in the format of the iteration logs.
When LOGFREQ=1, the following information is printed in the iteration log:
- Phase
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indicates whether the primal crossover (PC) or dual crossover (DC) technique is used.
- Iteration
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indicates the iteration number.
- Objective Value
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indicates the total amount by which the superbasic variables are off their bound. This value decreases to 0 as the crossover algorithm progresses.
- Time
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indicates the time elapsed (in seconds) since the beginning of the crossover algorithm.
- Entering Variable
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indicates the entering pivot variable. A slack variable that enters the basis is indicated by the corresponding row name followed by “(S)”.
- Leaving Variable
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indicates the leaving pivot variable. A slack variable that leaves the basis is indicated by the corresponding row name followed by “(S)”.
When you omit the LOGFREQ= option or specify a value greater than 1, only the phase, iteration, objective value, and time information are printed in the iteration log.
After all the superbasic variables have been eliminated, the crossover algorithm continues with regular primal or dual simplex iterations.