Notes on Constrained Optimization
نویسنده
چکیده
where X is taken to be a known or given feasible set. In particular, we are interested in identifying x∗ ∈ X such that f (x∗) realizes the above minimum, if such an x∗ exists. Typical constraints include bounds on x, such as X = {x ∈ Rn : ||x||6 R} for some R > 0, or linear inequality constraints such as X = {x ∈ Rn : Ax> b} for a matrix A and a column vector b. More examples will be discussed. In the usual way, we subsume the problem of maximization of f by instead minimizing − f . As in the previous notes, unless otherwise indicated we take f to be continuous, and at least twice differentiable over the domain. We additionally will largely restrict ourselves to constraint sets X that are closed; this will ensure that if f has a minimum value over X , it is realized by some point in the constraint set X . (Consider, for instance, trying to maximize the function x over the open interval X = (0,1).) This will not be a serious limitation in practice.
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تاریخ انتشار 2016