Introduction to Unconstrained Optimization - Scilab

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2.7 Notes and references . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 2.8 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 3 Answers <strong>to</strong> exercises 35 3.1 Answers for section 1.10 . . . . . . . . . . . . . . . . . . . . . . . . . 35 3.2 Answers for section 2.8 . . . . . . . . . . . . . . . . . . . . . . . . . . 36 Bibliography 40 Index 41 2
Copyright c○ 2008-2010 - Michael Baudin This file must be used under the terms of the Creative Commons Attribution- ShareAlike 3.0 Unported License: http://creativecommons.org/licenses/by-sa/3.0 3
Page 1: Introduction to Unconstrained Optim
Page 5 and 6: Optimization Discrete Parameters Co
Page 7 and 8: A subclass of optimization problems
Page 9 and 10: -->[ f , g , H ] = rosenbrock ( x0
Page 11 and 12: 3000 2500 2000 Z 1500 1000 500 0 2.
Page 13 and 14: f(x) strong local optimum weak loca
Page 15 and 16: The previous definition intuitively
Page 17 and 18: x 1 x 2 x 1 x 2 Figure 7: Convex se
Page 19 and 20: 0 0 Figure 11: Conic hulls f(x) f(y
Page 21 and 22: T f(x)+g(x) (y-x) f(x) x Figure 15:
Page 23 and 24: By hypothesis x = θy 1 + (1 − θ
Page 25 and 26: Proof. We assume that the Hessian m
Page 27 and 28: 5 4 3 2 1 Z 0 -1 -2 -3 -4 -5 5 4 3
Page 29 and 30: 2.0 1.5 1.0 20 0.5 10 0.0 5 2 2 5 -
Page 31 and 32: φ(α) α 2.0 1.5 -20 φ(α) -10 1.
Page 33 and 34: 6 20 4 2 0 -5 0 5 -2 -4 20 -6 -10 -
Page 35 and 36: 3 Answers to exercises 3.1 Answers
Page 37 and 38: C x 2 x 2 x 1 x 3 x 3 Figure 28: Co
Page 39 and 40: for all x, y ∈ C, then f is conve
Page 41 and 42: [2] Grégoire Allaire. Analyse num

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