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Unformatted text preview: Introduction to Optimization  IOE 310 Romesh Saigal Office Hours: Wed 1:303:00pm and by appointment, Room IOE 2883 E Mail Address: rsaigal@umich.edu GSI 1 Ankit Agarwal GSI 2: Yu Zhou MIDTERM Tuesday, October 23, 2007 FINAL Thursday, December 13, 2007, 1:303:30 pm. IOE 310 Fall 2007 INTRODUCTION TO OPTIMIZATION LINEAR PROGRAMMING SPECIAL LINEAR PROGRAMS NETWORK FLOWS DYNAMIC PROGRAMMING NONLINEAR PROGRAMMING IOE 310 Fall 2007 A QUICK REVIEW OF LINEAR ALGEBRA A Vector: is a vertical array of numbers like: x = 2 3 4 A matrix: two dimensional array of numbers like: A = 2 3 4 3 4 5 Scalar multiplication: 5 x = 10 15 20 and 10 A = 20 30 40 30 40 50 Addition: x + 1 1 1 = 3 4 5 and A + 1 1 1 1 1 1 = 3 4 5 4 5 6 IOE 310 Fall 2007 GEOMETRY OF ADDING VECTORS I u v u+v THE GEOMETRY OF ADDING VECTORS x1 x2 u v u+v Angle between u and v IOE 310 Fall 2007 Norm of a vector:  x  = ( n X i =1 x 2 i ) 1 2 Inner product of vectors: Let u = u 1 . . . u n and v = v 1 ....
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This note was uploaded on 04/02/2008 for the course IOE 310 taught by Professor Saigal during the Spring '08 term at University of Michigan.
 Spring '08
 Saigal

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