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Final Exam Review

# Final Exam Review - EAD 115 Numerical Solution of...

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EAD 115 Numerical Solution of Engineering and Scientific Problems David M. Rocke Department of Applied Science

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Multidimensional Unconstrained Optimization Suppose we have a function f() of more than one variable f(x 1 , x 2 , …, x n ) We want to find the values of x 1 , x 2 , …, x n that give f() the largest (or smallest) possible value Graphical solution is not possible, but a graphical picture helps understanding Hilltops and contour maps

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Methods of solution Direct or non-gradient methods do not require derivatives – Grid search – Random search – One variable at a time – Line searches and Powell’s method – Simplex optimization
Gradient methods use first and possibly second derivatives – Gradient is the vector of first partials – Hessian is the matrix of second partials – Steepest ascent/descent – Conjugate gradient – Newton’s method – Quasi-Newton methods

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Grid and Random Search Given a function and limits on each variable, generate a set of random points in the domain, and eventually choose the one with the largest function value Alternatively, divide the interval on each variable into small segments and check the function for all possible combinations