@article{Harvey2013,
  author = {Harvey, J.-P. and Eriksson, G. and Orban, D. and Chartrand, P.},
  doi = {10.2475/03.2013.02},
  issn = {0002-9599},
  journal = {Am. J. Sci.},
  keywords = {cluster site approximation,cluster variation method,complex phase equilibria,disorder phase,equilibrium phase assemblage estimation,gibbs energy minimization,order,phase stability evaluation,technique,transitions},
  month = {may},
  number = {3},
  pages = {199--241},
  title = {{Global minimization of the Gibbs energy of multicomponent systems Involving the presence of order/disorder phase transitions}},
  url = {http://www.ajsonline.org/cgi/doi/10.2475/03.2013.02},
  volume = {313},
  year = {2013},
}


@article{Hillert1981,
  author = {Hillert, M.},
  doi = {10.1016/0378-4363(81)91000-7},
  issn = {03784363},
  journal = {Phys. B+C},
  month = {jan},
  number = {1},
  pages = {31--40},
  title = {{Some viewpoints on the use of a computer for calculating phase diagrams}},
  url = {http://linkinghub.elsevier.com/retrieve/pii/0378436381910007},
  volume = {103},
  year = {1981},
}


@article{Halton_1964,
  doi = {10.1145/355588.365104},
  url = {http://dx.doi.org/10.1145/355588.365104},
  year = {1964},
  month = {dec},
  publisher = {Association for Computing Machinery ({ACM})},
  volume = {7},
  number = {12},
  pages = {701--702},
  author = {J. H. Halton},
  title = {{Algorithm 247: Radical-inverse quasi-random point sequence}},
  journal = {Communications of the {ACM}},
}


@article{Emelianenko_2006,
  doi = {10.1016/j.commatsci.2005.03.004},
  url = {http://dx.doi.org/10.1016/j.commatsci.2005.03.004},
  year = {2006},
  month = {jan},
  publisher = {Elsevier {BV}},
  volume = {35},
  number = {1},
  pages = {61--74},
  author = {Maria Emelianenko and Zi-Kui Liu and Qiang Du},
  title = {{A new algorithm for the automation of phase diagram calculation}},
  journal = {Computational Materials Science},
}


@article{Perevoshchikova_2012,
  doi = {10.1016/j.commatsci.2012.03.050},
  url = {http://dx.doi.org/10.1016/j.commatsci.2012.03.050},
  year = {2012},
  month = {aug},
  publisher = {Elsevier {BV}},
  volume = {61},
  pages = {54--66},
  author = {Nataliya Perevoshchikova and Beno{\^{\i}}t Appolaire and Julien Teixeira and Elisabeth Aeby-Gautier and Sabine Denis},
  title = {{A convex hull algorithm for a grid minimization of Gibbs energy as initial step in equilibrium calculations in two-phase multicomponent alloys}},
  journal = {Computational Materials Science},
}


@inproceedings{hess2003performance,
  title = {{On the performance of the shuffled Halton sequence in the estimation of discrete choice models}},
  author = {Hess, St{\'e}phane and Polak, John W and Daly, Andrew},
  booktitle = {European Transport Conference, Strasbourg},
  year = {2003},
}


@article{Lukas1982,
  author = {Lukas, H.L. and Weiss, J. and Henig, E.-Th.},
  doi = {10.1016/0364-5916(82)90004-9},
  issn = {03645916},
  journal = {Calphad},
  month = {jul},
  number = {3},
  pages = {229--251},
  title = {{Strategies for the calculation of phase diagrams}},
  url = {http://www.sciencedirect.com/science/article/pii/0364591682900049},
  volume = {6},
  year = {1982},
}


@book{Nocedal2006,
  address = {New York},
  author = {Nocedal, Jorge and Wright, Stephen},
  doi = {10.1007/978-0-387-40065-5},
  edition = {2},
  isbn = {978-0-387-30303-1},
  publisher = {Springer},
  series = {Springer Series in Operations Research and Financial Engineering},
  title = {{Numerical Optimization}},
  url = {http://link.springer.com/10.1007/978-0-387-40065-5},
  year = {2006},
}


@article{Woronow1993,
  abstract = {Algorithms for three types of random compositional vectors are provided in this article. The first is intuitive. Random basis (“open”) vectors are transformed into compositional vectors by dividing each vector's components by the sum of its components. The second algorithm uses a coordinate transformation to map uniform random vectors in a d-dimensional hypertetrahedron into uniformly distributed compositional variables on the d + 1 dimensional simplex. The third algorithm operates upon a logratio population covariance matrix and vector of means to produce random compositional vectors drawn from the same distribution. The statistical attributes of the crude compositional data also are honored by this method.},
  author = {Woronow, Alex},
  doi = {10.1016/0098-3004(93)90045-7},
  file = {:home/rotis/.local/share/data/Mendeley Ltd./Mendeley Desktop/Downloaded/Woronow - 1993 - Generating random numbers on a simplex.pdf:pdf},
  issn = {00983004},
  journal = {Comput. Geosci.},
  keywords = {Monte Carlo,Random numbers,Simplex,Simulations},
  mendeley-groups = {Global\_Min},
  month = {jan},
  number = {1},
  pages = {81--88},
  title = {{Generating random numbers on a simplex}},
  url = {http://www.sciencedirect.com/science/article/pii/0098300493900457},
  volume = {19},
  year = {1993},
}


@article{Chi2005,
  abstract = {Quasi-Monte Carlo methods are a variant of ordinary Monte Carlo methods that employ highly uniform quasirandom numbers in place of Monte Carlo’s pseudorandom numbers. Clearly, the generation of appropriate high-quality quasirandom sequences is crucial to the success of quasi-Monte Carlo methods. The Halton sequence is one of the standard (along with (t,s)-sequences and lattice points) low-discrepancy sequences, and one of its important advantages is that the Halton sequence is easy to implement due to its definition via the radical inverse function. However, the original Halton sequence suffers from correlations between radical inverse functions with different bases used for different dimensions. These correlations result in poorly distributed two-dimensional projections. A standard solution to this phenomenon is to use a randomized (scrambled) version of the Halton sequence. An alternative approach to this is to find an optimal Halton sequence within a family of scrambled sequences. This paper presents a new algorithm for finding an optimal Halton sequence within a linear scrambling space. This optimal sequence is numerically tested and shown empirically to be far superior to the original. In addition, based on analysis and insight into the correlations between dimensions of the Halton sequence, we illustrate why our algorithm is efficient for breaking these correlations. An overview of various algorithms for constructing various optimal Halton sequences is also given.},
  author = {Chi, H. and Mascagni, M. and Warnock, T.},
  doi = {10.1016/j.matcom.2005.03.004},
  issn = {03784754},
  journal = {Math. Comput. Simul.},
  keywords = {Correlation,Optimal Halton sequence,Quasi-Monte Carlo,Scrambling},
  mendeley-groups = {Global\_Min},
  month = {sep},
  number = {1},
  pages = {9--21},
  title = {{On the optimal Halton sequence}},
  url = {http://www.sciencedirect.com/science/article/pii/S037847540500087X},
  volume = {70},
  year = {2005},
}