An e-commerce company formulates a 100 000-variable, 5 000-constraint linear program to allocate ad impressions while respecting budget, pacing, and delivery limits. All coefficients are linear and the constraint matrix is extremely sparse. The team must repeatedly re-optimize the model every few minutes as new pricing data arrive. They decide to begin with a primal revised simplex solver rather than an interior-point solver.
Which technical consideration is the MOST defensible reason for choosing the revised simplex approach in this situation?
It updates all primal and dual variables simultaneously through a barrier-based KKT system at every iteration, giving lower memory growth than interior-point methods for large models.
It can easily warm-start from a previously optimal basis and exploit sparsity, so each re-optimization after a small data change typically needs only a few additional pivots.
It is the only approach that can provide dual shadow-price information; interior-point methods cannot return usable duals.
It keeps all basic variables strictly positive by adding logarithmic barrier terms, eliminating degeneracy problems seen with interior-point solvers.
The revised simplex method stores and updates a factorized basis of the constraint matrix, so each pivot only touches the two columns associated with the entering and leaving variables. This design makes it very efficient on large sparse problems and, crucially, it allows the solver to be warm-started: after a small change to the right-hand side or objective, the previous optimal basis is still close to optimal, so only a few additional pivots are needed. Interior-point methods, by contrast, follow a central path and re-factor a large KKT system every iteration; small data changes rarely let them re-use an earlier iterate effectively, so warm starts provide much less benefit.
Incorrect choices:
The use of logarithmic barrier terms to keep variables strictly positive is a hallmark of interior-point algorithms, not simplex.
Both solver families can return shadow prices/dual values; interior-point methods do so throughout the run, so the claim that they cannot is false.
Interior-point solvers, not revised simplex, update all primal and dual variables simultaneously via a barrier system each iteration; simplex pivots only update a small subset of variables.
Therefore, exploiting sparsity and reliable warm starts makes the revised simplex method the best initial choice.
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