References for term paper

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


Convex sets

[NPS2008] J. Nie, P.A. Parrilo, and B. Sturmfels, "Semidefinite Representation of the k-Ellipse",  In: Algorithms in Algebraic Geometry, Editors: A. Dickenstein, F.O. Schreyer, and A.J. Sommese. The IMA Volumes in Mathematics and its Applications, vol 146, pp. 117--132, 2008.
[RS2012] P. Rostalski, and B. Sturmfels, "Dualities", In: Semidefinite Optimization and Convex Algebraic Geometry, Editors: G. Blekherman , P.A. Parrilo, and R.R. Thomas, Ch. 5, 2012.

[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.