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# In the worst case however we still have to enumerate

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Unformatted text preview: tion is also closely related to which cost function one aims to use (See Table 1). This suggests that considering a discrete set of tolerances could be more suitable to a real-life situation. This does not make the problem any easier, despite what one might expect. Before we introduce the discrete tolerance allocation problem, we need a brief review of the field of discrete optimization and some common solution methods. An Efficient Solution 3. DISCRETE OPTIMIZATION A discrete optimization problem is to minimize f ( x ) over all x ∈ S , or short min f ( x ) x ∈ S, 119 (8) where f : X ⊃ S a R is an objective function and S is a set of objects of some discrete structure in the underlying space X. S ⊂ X is called the feasible set, and an object x ∈ S is called a feasible solution. An optimal solution x* ∈ S is a feasible solution such that f ( x* ) ≤ f ( x) for all x ∈ S . An optimization problem can either have an optimal solution or the problem is infeasible, that is if S is empty or if the problem is unbounded. If X is the set of all...
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## This note was uploaded on 08/03/2010 for the course DD 1234 taught by Professor Zczxc during the Spring '10 term at Magnolia Bible.

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