Introduction to Online Convex Optimization, Second Edition by Elad Hazan;

Author:Elad Hazan;
Language: eng
Format: epub
Tags: Machine learning; mathematical optimization; game theory; learning theory
Publisher: MIT Press

7.7 Exercises

1.   Prove that if the singular values are smaller than or equal to 1, then the nuclear norm is a lower bound on the rank. That is, show that

2.   Prove that the trace is related to the nuclear norm via

3.   Show that maximizing a linear function over the spectahedron can be reduced to a maximal eigenvector computation.

(a) Consider the the following mathematical program for a symmetric C ∈ℝd×d:

Prove that it has the same solution as the following mathematical program:

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