lec29_11222006 - 10.34, Numerical Methods Applied to...

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10.34, Numerical Methods Applied to Chemical Engineering Professor William H. Green Lecture #29: Global Optimization. Multiple Minima. Convex vs. Non-Convex Convex – only one minimum Non-convex – multiple relative minima min x f(x ) Global Optimization (Deterministic) x f(x ) Figure 1. A function with relative minima. Convex Underestimator x opt By looking at 2 nd derivatives, find parabola that is lower than other minimum. 2 3 Figure 2. Convex underestimator. Choose a f(x), upper bound. Divide domain. Underestimate the lower bound with a parabola. Find minimum of parabola. Bound again. If new upper bound is lower than lower bound in other region, can stop considering that section. Cite as: William Green, Jr., course materials for 10.34 Numerical Methods Applied to Chemical Engineering, Fall 2006. MIT OpenCourseWare (http://ocw.mit.edu), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].
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To converge – lower bound rises at a certain rate; upper bound decreases at a certain rate. Going several zones deep, creates many divisions: 2
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This note was uploaded on 11/27/2011 for the course CHEMICAL E 10.302 taught by Professor Clarkcolton during the Fall '04 term at MIT.

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lec29_11222006 - 10.34, Numerical Methods Applied to...

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