Guide for Week 9
Math 408 Section A
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Reading Assignment:
Homework Assignment:
- Finish all the problems in problem set 5.
- Find two linearly independant descent directions of the function f(x,y)=\sin(e^x+e^y) at the point (x,y)=(\ln(\pi/2),\ln(\pi/2)).
Vocabulary Words
- Optimality Conditions for Unconstrained Problems
- Extreme value theorem
- coercive functions
- compactness theorem
- The basic first-order optimality result
- The first-order necessary conditions for optimality
- the second-order necessary and sufficient conditions for optimality
- convex functions
- strongly convex functions
- the convexity and optimality theorem
- first- and second-order conditions for convexity checking
- gradients and Hessians of linear least squares functions and general
quadratic functions
- Line search methods
- Descent direction
- Steepest descent direction
- Newton method
- Backtracking line search
- Guarantees on the convergence of general line search methods
- Guarantees on the convergence of the steepest descent method and Newton method
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Skills to Master:
- computing derivatives and Taylor approximations
- locating and classifying critical points
- checking convexity
- running iterations of a line search method (steepest descent or Newton)
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Quiz:
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The quiz will consist of 2 questions, as usual.