### Table 1: Relationships Between Primal and Dual Problems (page 241 in [3])

"... In PAGE 3: ...2 Rules for Formulating the Dual In the dual of a linear program, there is one dual variable corresponding to one primal constraint, and one dual constraint for each primal variable. Table1 gives the rules in formulating the dual of a primal LP. Connection with Lagrange dual function (in x5.... ..."

### Table 5.2: Insights from the dual problem

### Table 4: Results for solving the dual GP problems.

1996

"... In PAGE 28: ... However, they only present results for solving small-sized GP problems and the results presented in [36] indicate that these methods may not be as e cient as \direct quot; primal-dual methods. In Table4 results for the GP dual (49) of the test problems are presented. First, the table shows the number of constraints and variables before and after presolve.... ..."

### Table 4: Results for solving the dual GP problems.

"... In PAGE 28: ... However, they only present results for solving small-sized GP problems and the results presented in [36] indicate that these methods may not be as e cient as \direct quot; primal-dual methods. In Table4 results for the GP dual (49) of the test problems are presented. First, the table shows the number of constraints and variables before and after presolve.... ..."

### Table 5: Accuracy results for the dual GP problems.

1996

### Table 5: Accuracy results for the dual GP problems.

### Table 3 Dual degenerate problem: m = 6;n = 12;jBj = 8 k

1997

"... In PAGE 22: ... Our second example is for a dual degenerate problem with jBj = 8 gt; m. As can be seen from Table3 , the algorithm achieves fairly high accuracy after about 20 iterations, but no further improvement can be made after that point. The behavior is consistent with the discussion of Section 9.... ..."

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### Table 3 Primal Dual

"... In PAGE 10: ... If the ith primal variable yi is urs, the ith dual constraint is an equality constraint. Table3 gives a more complete relationship between nonnormal primal and dual problems. Table 3 Primal Dual... ..."

### Table 2.1. Transformation between primal and dual Exercise 2.9. Find the dual of problem (P) in Example 2.2, and show that it has the optimal value fD(y )=108. Example 2.10. The roles of the primal and dual problem may interchange: Consider the LO problem from Example 2.8. It can be written as (Q)

### Table 4.1: Dual algebraic approaches for primal and dual multidimensional transporta- tion problems of several types.

2002