Foundations of Optimization

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Springer Science & Business Media, Aug 3, 2010 - Business & Economics - 442 pages
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This book covers the fundamental principles of optimization in finite dimensions. It develops the necessary material in multivariable calculus both with coordinates and coordinate-free, so recent developments such as semidefinite programming can be dealt with.

 

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Contents

1 Differential Calculus
1
2 Unconstrained Optimization
31
3 Variational Principles
61
4 Convex Analysis
84
5 Structure of Convex Sets and Functions
117
6 Separation of Convex Sets
140
7 Convex Polyhedra
175
8 Linear Programming
194
11 Duality Theory and Convex Programming
274
12 Semiinfinite Programming
313
13 Topics in Convexity
335
14 Three Basic Optimization Algorithms
361
A Finite Systems of Linear Inequalities in VectorSpaces
407
B Descartess Rule of Sign
413
C Classical Proofs of the Open Mapping and Gravess Theorems
416
References
421

9 Nonlinear Programming
209
10 Structured Optimization Problems
251

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