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UNIVERSITY OF WATERLOO Nonlinear Optimization (CO 367)
 

Summary: UNIVERSITY OF WATERLOO
Nonlinear Optimization (CO 367)
E. de Klerk, C. Roos, and T. Terlaky
Waterloo, February 23, 2006
Contents
0 Introduction 1
0.1 The general nonlinear optimization problem . . . . . . . . . . . . . . . . . . . . . . . . . 1
0.2 A short history of nonlinear optimization . . . . . . . . . . . . . . . . . . . . . . . . . . 3
0.3 Some historical examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
0.3.1 Tartaglia's problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
0.3.2 Kepler's problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
0.3.3 Steiner's problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
0.4 Quadratic optimization examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
0.4.1 The concrete mixing problem: least square estimation . . . . . . . . . . . . . . . 6
0.4.2 Portfolio analysis (mean­variance models) . . . . . . . . . . . . . . . . . . . . . . 7
1 Convex Analysis 9
1.1 Convex sets and convex functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
1.2 More on convex sets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
1.2.1 Convex hulls and extremal sets . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
1.2.2 Convex cones . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

  

Source: Al Hanbali, Ahmad - Department of Applied Mathematics, Universiteit Twente

 

Collections: Engineering