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Unformatted text preview: MATHEMATICS 116, FALL 2007 CONVEXITY AND OPTIMIZATION WITH APPLICATIONS Outline #9 (Inequality Constraints) Last modified: December 18, 2007 Reading. Luenberger, Chapter 8. If you want to understand the term projects, you should work through these simple examples, then skim the chapter. This is all optional material, not required for the final exam! Lecture topics. 1. Positive cones (Luenberger Section 8.2) Luenberger wants to have several Lagrange multipliers, refer to them as a single vector z * , and say that z * 0. This can be done by introducing a positive cone P . The simplest example (and the only one we will need for the moment, is the positive orthant, the set of vectors in E n whose components are all nonnegative. Any vector in p is called positive. How can you now assign a meaning to x y for vectors? What properties of for real numbers carry over to vectors? What important property of for real numbers does not carry over to vectors?...
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This document was uploaded on 08/30/2011.
 Fall '09
 Math

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