Reading a Simplex Solver Log

Learn to interpret the diagnostic output produced by a simplex LP solver — the header with problem statistics, the per-iteration log of objective and infeasibility values, and the final termination status — and synthesize all three to extract optimal value, phase counts, and matrix density from a full log.

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Tutorial

Anatomy of a Solver Log

A simplex solver log is the diagnostic text a solver prints while running. It is organized into three blocks:

Header — problem dimensions after preprocessing.
Iteration log — one line per recorded pivot, showing progress.
Termination message — a one-line verdict.

A typical header line is

$\texttt{3 rows, 4 columns, 8 non-zeros}$

The rows count is the number of constraints in the LP, the columns count is the number of decision variables, and non-zeros is the count of nonzero entries in the constraint matrix $A.$

The density of $A$ is

\text{density} = \dfrac{\text{nonzeros}}{\text{rows} \times \text{columns}}.

For the header above, the density is $\dfrac{8}{3 \cdot 4} = \dfrac{8}{12} \approx 66.7\%.$ Real-world LPs are usually far sparser — often well under $1\%$ — which is precisely why revised simplex stores and factors $A$ using sparse data structures.