eldo_user

Optimization
Normal and Elastic Modes of Termination
Section 3 - Status Of Objectives
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*** Inequality Constraints in simulator id(0)
Type Name Init Value Opt Value Violation
UPR CONSTR1 *** 1.1000e+01 1.0000e-06 *** 1.0000e+00
The optimal value is 1.0×10 −6 and the violation (or equivalently the value of the additional
variable v) is shown in the last column as being the strictly positive value 1.0.
Note
This approach has very interesting properties. For instance, the optimal solution often
violates only a small number of the constraints and a point that satisfies many of the
constraints is computed, that is, a large subset of constraints that are feasible have been
identified. This is more informative than finding that the constraints are mutually feasible (this
approach is closely related to the L1-norm regularization technique).
Related Topics
Slack
Slack
For this next example, consider the following problem with two variables. The aim is to
minimize some function f(x 1 , x 2 ) subject to the constraints:
• (x 1 + 1) 2 + x 2 2 ≥ 0.75 which defines a disk centered at (-1, 0) with radius √3/2.
• (x 1 − 1) 2 + x 2 2 ≤ 0.75 which defines the symmetrical disk centered at (1, 0).
Figure 13-19 illustrates this situation.
Eldo® User's Manual, 15.3 661