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lecture_1 - Introduction to Optimization IOE 310 Romesh...

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Introduction to Optimization - IOE 310 Romesh Saigal Office Hours: Wed 1:30-3:00pm and by appointment, Room IOE 2883 E Mail Address: [email protected] GSI 1 Ankit Agarwal GSI 2: Yu Zhou MIDTERM Tuesday, October 23, 2007 FINAL Thursday, December 13, 2007, 1:30-3:30 pm. IOE 310 Fall 2007
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INTRODUCTION TO OPTIMIZATION LINEAR PROGRAMMING SPECIAL LINEAR PROGRAMS NETWORK FLOWS DYNAMIC PROGRAMMING NONLINEAR PROGRAMMING IOE 310 Fall 2007
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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
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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
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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 . . . v n then u T v = n X i =1 u i v i where v T is the vector v written as a row, called the transpose of v .
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