eldo_user

Optimization
Normal and Elastic Modes of Termination
Normal and Elastic Modes of Termination
The SQP algorithm is able to make explicit allowance for infeasible constraints when
computing the incremental steps obtained from a sequence of sub-problems. This phenomenon
is referred to as local infeasibility.
In constrained optimization, a situation where no feasible solution exists can occur. In this case
the constraints are inconsistent and the problem is infeasible. If all the constraints are bounds on
the variables x
(i)
l ≤ x (i) ≤ x
(i)
u it is simple to determine whether a feasible point exists, since the
(i)
ith is only inconsistent when x l > x (i) u . Such infeasibilities are automatically trapped when
parsing the .PARAMOPT command.
Conversely, with general constraints there are no simple characteristics that identify whether a
feasible solution exists.
This section describes how the algorithm performs a shift of bounds on objectives to make a
locally infeasible problem feasible. It handles:
Constraint Violations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 659
Slack . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 661
Constraint Violations
The following simple example illustrates one possible situation.
Consider the optimization problem with two variables x 1 and x 2 :
.PARAMOPT X1=(4, 0, *)
.PARAMOPT X2=(7, 0, *)
.OBJECTIVE DC LABEL=C (X1 + X2) UBOUND=-1
These statements define two bound constraints on the variables x 1 ≥ 0 and x 2 ≥ 0, and the linear
constraint on the measure x 1 + x 2 ≤ -1.
By considering the graphical representation displayed in the left part of Figure 13-18, you can
see that they define two disjoint sets of points. The optimization problem is thus infeasible.
Eldo® User's Manual, 15.3 659