eldo_user

Optimization
Normal and Elastic Modes of Termination
The column Slack is the value of the global constraint violation — the norm of the artificial
variables (v 1 , v 2 ) added to the upper bound UBOUND for each constraint. The constraints
become:
• (x 1 + 1) 2 + x 2
2
≥ 0.75 + v 1 .
• (x 1 − 1) 2 + x 2
2
≤ 0.75 + v 2 .
The value of the slack becomes strictly positive after the 6th iteration. This phenomenon can be
interpreted as follows:
• After the 6th iteration the algorithm detected that the problem is locally infeasible.
• Two artificial variables are then introduced such that the constraints become consistent.
Graphically, this can be interpreted as increasing the radius of the two circles such that
they do intersect.
• The goal of the algorithm is then to find a solution point such that the constraint
violation is minimized.
The final solution is given in the following output:
Section 2 - Status Of Variables
-------------------------------
Name Status Init Value Final Value
X1 FR -2.0000e+00 -5.0009e-07
X2 FR -2.0000e+00 1.6166e-05
Section 3 - Status Of Objectives
--------------------------------
*** Inequality Constraints in simulator id(0)
Type Name Init Value Opt Value Violation
UPR CIRCLE1 *** 1.3000e+01 1.0000e+00 *** 2.5000e-01
UPR CIRCLE2 *** 5.0000e+00 1.0000e-00 *** 2.5000e-01
Constraint violations have been minimized. The actual value of the violation is v 1 = 0.25 for the
first constraint and v 2 = 0.25 for the second. The solution point is approximately the origin (0,
0). The algorithm automatically increased the radius of each circle such that the feasible domain
becomes a non empty set. The feasible set reduces to the singleton (0, 0).
Related Topics
Constraint Violations
Eldo® User's Manual, 15.3 663