Feasibility
Consider the simple problem
Feasibility requires
for all k.
FSQP generates iterates that
satisfy all inequality constraints and linear equality constraints.
Why feasibility?
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From an application point of view:
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Objective may not be defined if certain constraints
are violated. For example, the steady-state errors
of a dynamical system are undefined if the system
is not stable. Important for real-time applications.
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May have to terminate the optimization process after
a prescribed amount of time, in which case it may
be crucial that the sub-optimal solution at least
satisfy some hard constraints.
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In the context of optimal design, tradeoff exploration
cannot meaningfully take place if some hard constraints
are not first satisfied. It is thus of great interest
to produce iterates that all satisfy these hard
constraints.
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From an algorithmic point of view:
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The line search criterion can be based on the decrease
of the objective function, i.e., there is no need
for an artifical "merit function".
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In the SQP context, whenever the current iterate
is feasible, the QP subproblem has a feasible solution.
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