# assn1 - MIT OpenCourseWare http://ocw.mit.edu 16.323...

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Unformatted text preview: MIT OpenCourseWare http://ocw.mit.edu 16.323 Principles of Optimal Control Spring 2008 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms . 16.323 Handout #1 Prof. J. P. How Feb 7, 2008 Due: Feb 21, 2008 16.323 Homework Assignment #1 Any code for this homework should be submitted online using the class web page- do not forget, as it will be graded as part of your solution. 1. For the following function, F ( x 1 , x 2 , x 3 ) = 2 x 1 4 + 3 x 2 2 + 6 x 3 2 − 3 x 1 x 2 − 6 x 2 x 3 (a) Find the minimum(s). (b) Are there any other stationary points? If so, what are they? 2. Give the criteria used to determine if a symmetric real matrix is negative definite or positive semidefinite, in terms of 1) eigenvalues and 2) determinants of respective submatrices. 3. This problem explores the steepest descent algorithm. For the following function, F ( x 1 , x 2 , x 3 ) = x 1 2 + x 2 2 + x 3 2 − x 1 x 2 − x 2 x 3 − 2 x 1 − 8 x 3 (a) Give an expression...
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## This note was uploaded on 11/07/2011 for the course AERO 16.323 taught by Professor Jonathanhow during the Spring '08 term at MIT.

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assn1 - MIT OpenCourseWare http://ocw.mit.edu 16.323...

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