The solution process is iterative. It begins at the starting values and ends at the final values. At each iteration, Embed attempts to improve the objective function. If the problem is not feasible, Phase I may result in an objective function that is worse than the starting value, but this is necessary to achieve feasibility.
Column 
Heading 
Description 
1 
Itn No. 
Iteration number. 
2 
Objective Function 
Value of the objective function. If some constraints are not feasible (see column 5), the objective function value is the sum of the constraint violations. 
3 
Binding Constrs 
Number of constraints that are at either their lower or upper bound. The binding constraints provide a set of nonlinear equations that can be used to solve some of the variables in terms of other variables. See also Super Basics. 
4 
Super Basics 
Independent variables of the reduced problem. Variables are classified by Embed as basic, nonbasic, and superbasic, as described later under “Final Results section.” 
5 
Infeas Constr 
Number of infeasible constraints; that is, the constraints that violate their bounds for the current values of the variables. 
6 
Norm of Red. Grad 
Norm of the reduced gradient; also referred to as the KuhnTucker factor or the KT factor. This number is the maximum absolute value of gradient of the reduced objective function with respect to the set of superbasic variables scaled by the value of the variable and the inverse of the value of the objective function. When the value of the KT factor is less than epstop (the stopping criteria), Embed terminates the iteration and returns the current variable values. 
7 
Hessian Cond. No. 
Condition number of the Hessian. The Hessian is the matrix of second derivatives of the objective function with respect to the variables. A large condition number indicates an illconditioned problem that may be difficult to solve accurately. 
8 
Step Size 
Step size for the current iteration. 
9 
Degen Step 
A “T” in this column indicates a degenerate step (iteration); otherwise this column is blank. When Embed reclassifies variables from basic to superbasic and from superbasic to basic, the objective function does not change and the iteration is flagged as degenerate to avoid the appearance of convergence. 
Itn 
Objective 
Binding 
Super 
Infeas 
Norm of 
Hessian 
Step 
Degen 
No. 
Function 
Constrs 
Basics 
Constr 
Red.Grad 
Cond.No. 
Size 
Step 
___ 
_________ 
________ 
______ 
______ 
________ 
_______ 
____ 
_____ 
0 
0.178051 
0 
2 
0 
0.39 
1 
1 

1 
0.100372 
1 
1 
0 
0.081 
1 
0.2 

2 
0.0621484 
1 
1 
0 
0.00011 
1 
0.51 
