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Solving Optimization Problems with MATLAB

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1 2018 The MathWorks, Optimization Problems with MATLAB2 Introduction Least-squares minimization Nonlinear Optimization Mixed-integer programming Global optimizationTopics3Optimization ProblemsMinimize RiskMaximize ProfitsMaximize Fuel Efficiency4Design ProcessInitial Design VariablesSystemModify Design VariablesOptimal DesignObjectivesmet?NoYes5Manually (trial-and-error or iteratively)Why use Optimization ?Initial Guess6Automatically (using optimizationtechniques)Initial GuessWhy use Optimization ?7Why use Optimization ? Finding better (optimal) designs and decisions Faster design and decision evaluations Automate routine decisions Useful for trade-off analysis Non-intuitive designs may be foundAntenna Design Using Genetic Introduction Least-squares minimization Nonlinear Optimization Mixed-integer programming Global optimizationTopics9Curve Fitting DemoGiven some data:Fit a curve of the form:teccty 21)(t = [0.]

Apply pattern vector, poll new points for improvement x y 3 Mesh size = 1 Pattern vectors = [1,0], [0,1], [-1,0], [0,-1] Pnew mesh_ size* pattern_ vector x 0 1*[1,0] x 0 1.6 0.4 4.6 2.8 First poll successful Complete Poll (not default)

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