Bibliographic Notes#

Following is a partial list of books and articles which have been referenced heavily in this work. This list is by no means exhaustive.

  • General introduction to optimization can be found in [18].

  • Main references for convex analysis are [5, 20].

  • [8] is a standard textbook for convex optimization theory, applications and algorithms.

  • [17] is a good reference for linear programming.

  • [7] covers alternating direction method of multipliers (ADMM) algorithms.

  • [19] provides good coverage on proximal algorithms.

Bibliography#

1

Charalambos D Aliprantis and Owen Burkinshaw. Principles of real analysis. Gulf Professional Publishing, 1998.

2

M. Artin. Algebra. Pearson Modern Classics for Advanced Mathematics Series. Pearson, 2017. ISBN 9780134689609. URL: https://books.google.co.in/books?id=ZfIXMQAACAAJ.

3

Amir Beck. Introduction to nonlinear optimization: Theory, algorithms, and applications with MATLAB. SIAM, 2014.

4

Amir Beck. First-order methods in optimization. SIAM, 2017.

5

Dimitri Bertsekas, Angelia Nedic, and Asuman Ozdaglar. Convex analysis and optimization. Volume 1. Athena Scientific, 2003.

6

Stephen Boyd and Almir Mutapcic. Subgradient methods. 2008.

7

Stephen Boyd, Neal Parikh, and Eric Chu. Distributed optimization and statistical learning via the alternating direction method of multipliers. Now Publishers Inc, 2011.

8

Stephen P Boyd and Lieven Vandenberghe. Convex optimization. Cambridge university press, 2004.

9

Emmanuel J Candes and Terence Tao. Decoding by linear programming. Information Theory, IEEE Transactions on, 51(12):4203–4215, 2005.

10

Emmanuel J Candes and Terence Tao. Near-optimal signal recovery from random projections: universal encoding strategies? Information Theory, IEEE Transactions on, 52(12):5406–5425, 2006.

11

David L Donoho and Michael Elad. Optimally sparse representation in general (nonorthogonal) dictionaries via $l_1$ minimization. Proceedings of the National Academy of Sciences, 100(5):2197–2202, 2003.

12

Michael Elad. Sparse and redundant representations. Springer, 2010.

13

Michael Elad and Alfred M Bruckstein. A generalized uncertainty principle and sparse representation in pairs of bases. Information Theory, IEEE Transactions on, 48(9):2558–2567, 2002.

14

D. Gopal, A. Deshmukh, A.S. Ranadive, and S. Yadav. An Introduction to Metric Spaces. CRC Press, 2020. ISBN 9781000087994. URL: https://books.google.co.in/books?id=13jtDwAAQBAJ.

15

Jean-Baptiste Hiriart-Urruty and Claude Lemaréchal. Convex analysis and minimization algorithms I: Fundamentals. Volume 305. Springer science & business media, 2013.

16

Kenneth Hoffman and Ray Kunze. Linear algebra, prentice-hall. Inc., Englewood Cliffs, New Jersey, pages 122–125, 1971.

17

David G Luenberger, Yinyu Ye, and others. Linear and nonlinear programming. Volume 2. Springer, 1984.

18

Jorge Nocedal and Stephen Wright. Numerical optimization. Springer Science & Business Media, 2006.

19

Neal Parikh and Stephen Boyd. Proximal algorithms. Foundations and Trends in optimization, 1(3):127–239, 2014.

20

Ralph Tyrell Rockafellar. Convex analysis. Princeton university press, 2015.

21

W.F. Trench. Introduction to Real Analysis. Open Textbook Library. Prentice Hall/Pearson Education, 2003. ISBN 9780130457868. URL: https://books.google.co.in/books?id=NkFkQgAACAAJ.

22

Joel A Tropp. Greed is good: algorithmic results for sparse approximation. Information Theory, IEEE Transactions on, 50(10):2231–2242, 2004.

23

Joel A Tropp. Just relax: convex programming methods for subset selection and sparse approximation. ICES report, 2004.

24

Joel A Tropp. Just relax: convex programming methods for identifying sparse signals in noise. Information Theory, IEEE Transactions on, 52(3):1030–1051, 2006.

25

Wikipedia contributors. Ordered pair — Wikipedia, the free encyclopedia. URL: https://en.wikipedia.org/wiki/Ordered_pair.

26

Wikipedia contributors. Relation (mathematics) — Wikipedia, the free encyclopedia. URL: https://en.wikipedia.org/wiki/Relation_(mathematics).

27

Wikipedia contributors. Tuple — Wikipedia, the free encyclopedia. URL: https://en.wikipedia.org/wiki/Tuple.