Lecture13 - Advanced Mathematical Programming IE417 Lecture...

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Advanced Mathematical Programming IE417 Lecture 13 Dr. Ted Ralphs
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IE417 Lecture 13 1 Reading for This Lecture Chapter 7
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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 non-linear 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.
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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.
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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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