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Unformatted text preview: Advanced Mathematical Programming IE417 Lecture 13 Dr. Ted Ralphs IE417 Lecture 13 1 Reading for This Lecture • Chapter 7 IE417 Lecture 13 2 Iterative Algorithms • In previous courses, we have discussed algorithms that were guaranteed to terminate in a finite number of steps, usually with an optimal solution. • For nonlinear optimization, things are not so nice. • We will be dealing with iterative algorithms that produce an infinite sequence of points. • These algorithms may or may not converge to the optimal solution. IE417 Lecture 13 3 Properties of Iterative Algorithms • We will be interested in the following properties of an algorithm: – Does the algorithm converge? * Under what conditions does the algorithm converge? * Does it converge to a global optimal solution? * Does it converge to a local optimal solution? – How quickly does it converge? – How much computational effort is involved in each iteration? – How robust is the algorithm? • We will also be interested in the termination criteria and the accuracy of the solution. IE417 Lecture 13 4 The Algorithmic Map • An algorithm is defined by its algorithmic map . • Given our current location, where do we go next? • This is determined by a mapping A : X → 2 X which maps each point in the domain X to a set of possible “next iterates.” • In other words, if the current iterate is x k , then x k +1 ∈ A ( x k ) ....
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 Fall '08
 Linderoth
 Topology, Compact space, Closed set, limit point, xk, Iterative Algorithms

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