Convex Optimization

Please choose any one of the following references for your term paper.

**Convex sets**

**[HN2009]** J.W. Helton, and J. Nie, "Sufficient and necessary conditions for semidefinite representability of convex hulls and sets", *SIAM Journal on Optimization*, Vol. 20, No. 2, pp. 759--791, 2009.

**Convex functions and applications**

[BMDG2005] A. Banerjee, S. Merugu, I.S. Dhillon, and J. Ghosh, "Clustering with Bregman divergences", *Journal of Machine Learning Research*, Vol. 6, pp. 1705--1749, 2005.

[L2011] Y. Lucet, "What shape is your conjugate? A survey of computational convex analysis and its applications", *SIAM Review*, Vol. 52, No. 3, pp. 505--542, 2011.

**[LCBEJ2004]** G.R.G. Lanckriet, N. Cristianini, P. Bartlett, L. El Ghaoui, M.I. Jordan, "Learning the kernel matrix with semidefinite programming", *Journal of Machine Learning Research*, Vol. 5, pp. 27--72, 2004.

Convex optimization problems

**[GW1995]** M.X. Goemans, and D.P. Williamson, "Improved approximation algorithms for maximum cut and satisfiability problems using semidefinite programming",* Journal of the ACM*, Vol. 42, No. 6, pp. 1115--1145, 1995.

**[FGKM2018]** M. Fazel, R. Ge, S. Kakade, and M. Mesbahi, "Global convergence of policy gradient methods for the linear quadratic regulator", *Proceedings of the 35th International Conference on Machine Learning*, 80:1467-1476, 2018.

**[LVBH1998]** M.S. Lobo, L. Vanderberghe, S. Boyd, and L. Hervé, "Applications of second-order cone programming", *Linear Algebra and Its Applications*, Vol. 284, No. 1--3, pp. 193--228, 1998.

**[CR2009]** E. Candès, and B. Recht, "Exact matrix completion via convex optimization", *Foundations of Computaional Mathematics*, Vol. 9, No. 6, pp. 717--772, 2009.

**[LL2011]** J. Lavaei, and S. Low, "Zero duality gap in optimal power flow problem", *IEEE Transactions on Power Systems*, Vol. 27, No. 1, pp. 92--107, 2011.

**[VBW1998]** L. Vanderberghe, S. Boyd, and S.-P. Wu, "Determinant maximization with linear matrix inequality constraints", *SIAM Journal on Matrix Analysis and Applications*, Vo. 19, No. 2, pp. 499--533, 1998.

**[BKVH2007]** S. Boyd, S.J. Kim, L Vandenberghe, A Hassibi, "A tutorial on geometric programming", *Optimization and Engineering*, Vol. 8, No. 1, pp. 67--127, 2007.

**[EK2018]** P.M. Efsahani, and D. Kuhn, "Data-driven distributionally robust optimization using the Wasserstein metric: performance guarantees and tractable reformulations", *Mathematical Programming*, Vol. 171, pp. 115--166, 2018.

**[ABBS2020]** A. Agrawal, S. Barratt, S. Boyd, B. Stellato, "Learning Convex Optimization Control Policies", *Proceedings of the 2nd Conference on Learning for Dynamics and Control, PMLR*, Vol. 120, pp. 361--373, 2020.

Algorithms

[SBC2014] W. Su, S. Boyd, and E. Candès, "A differential equation for modeling Nesterov’s accelerated gradient method: Theory and insights", *Advances in Neural information processing systems*, pp. 2510--2518, 2014.

**[VA2015]** L. Vanderberghe, and M.S. Anderson, "Chordal graphs and semidefinite optimization", *Foundations and Trends in Optimization*, Vol. 1, No. 4, pp. 241--433, 2015.

**[BPCPE2010]** S. Boyd, N. Parikh, E. Chu, B. Peleato, and J. Eckstein, "Distributed optimization and statistical learning via the alternating direction method of multipliers", *Foundations and Trends in Machine Learning*, Vol. 3, No. 1, pp. 1--122, 2010.

**[BM2003]** S. Burer, and R.D. Monteiro, "A nonlinear programming algorithm for solving semidefinite programs via low-rank factorization", *Mathematical Programming*, Vo. 95, No. 2, pp. 329--357, 2003.

**[LRP2016]** L. Lessard, B. Recht, and A. Packard, "Analysis and design of optimization algorithms via integral quadratic constraints", *SIAM Journal on Optimization*, Vol. 26, No. 1, pp. 57--95, 2016.