Comments (1)
This formulation is fine, but maybe we can make it otherwise.
Another way to put it is IMHO to take linear constraints, i.e. E.x = f
, as the "base" construction object for both tasks and constraints (ignoring the case of inequality constraints for this discussion).
Then an objective can be associated to this constraint, e.g. || E.x - f ||^2
.
The advantage is twofold:
- we do not have confusing "minus" signs everywhere;
- we can easily transform any constraint into a task (might be useful for control purposes).
Actually we might have something like functions, constraints on functions, and metrics on constraints:
- [Function,
y := foo(x)
] <-- [Linear function,y := E.x
] - [Ineq constraint,
c := y - f < 0
] , [Equality constraint,c := y - f = 0
] - [Square eq constraint norm,
|| c ||^2
]
(- [Square ineq constraint norm,|| c ||^2 if c > 0, 0 otherwise
])
A classic quadratic task would then be a "square equality constraint norm" on an "equality constraint".
At any point in time we could convert this task into a constraint if needed, and vice-versa.
That would be useful also to transition on equality constraints activation by creating a task on it temporarily.
Note: this moves the question to whether y = f
or y = 0
is the proper way to write an equality constraint. In the former we only need linear functions y := E.x
, in the latter affine functions y := Ex +/- f
...
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