Lecture-1 - COT6505 Computational Methods Instructor: Dr....

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1 COT6505 Computational Methods Instructor: Dr. Mubarak Shah, shah@cs.ucf.edu , office:238 CSB , http://www.cs.ucf.edu/class/cap6411 Office Hours: 2PM to 3PM Mon, 4PM-5PM Tu, 3PM-4PM Thurs Grading – Mid term 25%, Final 35%, assignments (homework, programs),40% Text Book – Numerical Optimization, Jorge Nocedal and S. Wright, Springer, 1999. Other suggested Books – Numerical Analysis, Burden and Faires, PWS Kent. – Numerical Recipes in C, W. Press et al, Cambridge University press. Optimization • People optimize – Stocks – Job – exam • Convert qualitative description into quantitative function – Objective function – Variables – constraints
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2 Examples • Transportation problem • Camera Pose estimation in Computer Vision • Chess playing • Robot path planning • Computing the optimal shape of an automobile or aircraft • Controlling a chemical process or a mechanical device to optimize or meet standards of robustness Optimization • Minima, maxima or zero of a function • Local minima vs global minima
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3 Optimization Problems • Single variable • Multiple variables • Linear • Non-linear • Constraint optimization • Unconstraint optimization { 2 , 0 subject to ) 1 ( ) 2 min( 2 1 2 2 1 2 2 2 1 + - - + - x x x x x x Desirable Properties • Robustness • Efficiency • Accuracy
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4 Solution
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Lecture-1 - COT6505 Computational Methods Instructor: Dr....

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