@article{karmarkar_new_1984,
	title = {A new polynomial-time algorithm for linear programming},
	volume = {4},
	issn = {0209-9683, 1439-6912},
	url = {https://link.springer.com/article/10.1007/BF02579150},
	doi = {10.1007/BF02579150},
	abstract = {We present a new polynomial-time algorithm for linear programming. In the worst case, the algorithm requiresO(n3.5L) arithmetic operations onO(L) bit numbers, wheren is the number of variables andL is the number of bits in the input. The running-time of this algorithm is better than the ellipsoid algorithm by a factor ofO(n2.5). We prove that given a polytopeP and a strictly interior point a εP, there is a projective transformation of the space that mapsP, a toP′, a′ having the following property. The ratio of the radius of the smallest sphere with center a′, containingP′ to the radius of the largest sphere with center a′ contained inP′ isO(n). The algorithm consists of repeated application of such projective transformations each followed by optimization over an inscribed sphere to create a sequence of points which converges to the optimal solution in polynomial time.},
	language = {en},
	number = {4},
	urldate = {2017-04-08},
	journal = {Combinatorica},
	author = {Karmarkar, N.},
	month = dec,
	year = {1984},
	pages = {373--395},
	file = {karmarkar.pdf:/Users/ngolowich/Library/Application Support/Zotero/Profiles/7c93qi5d.default/zotero/storage/3KABFS7M/karmarkar.pdf:application/pdf;Snapshot:/Users/ngolowich/Library/Application Support/Zotero/Profiles/7c93qi5d.default/zotero/storage/C2JTSX9A/BF02579150.html:text/html}
}

@article{renegar_polynomial-time_1988,
	title = {A polynomial-time algorithm, based on {Newton}'s method, for linear programming},
	volume = {40},
	issn = {0025-5610, 1436-4646},
	url = {https://link.springer.com/article/10.1007/BF01580724},
	doi = {10.1007/BF01580724},
	abstract = {A new interior method for linear programming is presented and a polynomial time bound for it is proven. The proof is substantially different from those given for the ellipsoid algorithm and for Karmarkar's algorithm. Also, the algorithm is conceptually simpler than either of those algorithms.},
	language = {en},
	number = {1-3},
	urldate = {2017-04-08},
	journal = {Mathematical Programming},
	author = {Renegar, James},
	month = jan,
	year = {1988},
	pages = {59--93},
	file = {Snapshot:/Users/ngolowich/Library/Application Support/Zotero/Profiles/7c93qi5d.default/zotero/storage/PGAIQJ2X/10.html:text/html}
}

@misc{lee_path_2014,
	title = {Path {Finding} {Methods} for {Linear} {Programming}: {Solving} {Linear} {Programs} in $\sqrt{rank}$ {Iterations} and {Faster} {Algorithms} for {Maximum} {Flow}},
	url = {http://ieeexplore.ieee.org/document/6979027/},
	urldate = {2017-04-08},
	year={2014},
	author={Lee, Yin Tat and Sinford, Aaron},
	file = {Path Finding Methods for Linear Programming\: Solving Linear Programs in Õ(vrank) Iterations and Faster Algorithms for Maximum Flow - IEEE Xplore Document:/Users/ngolowich/Library/Application Support/Zotero/Profiles/7c93qi5d.default/zotero/storage/6R459RFA/6979027.html:text/html}
}