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Machine Learning
book

Machine Learning

by Sergios Theodoridis
April 2015
Intermediate to advanced content levelIntermediate to advanced
1062 pages
40h 35m
English
Academic Press
Content preview from Machine Learning
Appendix C

Hints on Constrained Optimization

Chapter Outline

C.1 Equality Constraints 1023

C.2 Inequality Constraints 1025

The Karush-Kuhn-Tucker (KKT) conditions 1025

Min-Max duality 1026

Saddle point condition 1027

Lagrangian duality 1027

Convex programming 1028

Wolfe dual representation 1029

References 1029

C.1 Equality Constraints

We will first focus on linear equality constraints and then generalize to the nonlinear case. The problem is cast as

minθJ(θ),s.t.Aθ=b,

si1_e

where A is an m × l matrix and b, θ are m × 1 and l × 1 vectors, respectively. It is assumed that the cost function J(θ) is twice continuously differentiable and it is, in general, ...

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Publisher Resources

ISBN: 9780128015223