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 Kuhn-Tucker factor or the K-T 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 K-T 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 ill-conditioned 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 |
|