Several research papers have been written which discuss the algorithms employed in MOSEK. Below is a list of those papers.
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E. D. Andersen, C. Roos and T. Terlaky,
On implementing a primal-dual interior-point method for conic quadratic optimization,
Math. Programming 95(2), February 2003
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E. D. Andersen,
Certificates of primal and dual infeasibility in linear programming,
Computational Optimization and Applications 20(2):171--183, 2001
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E. D. Andersen,
On primal and dual infeasibility certificates in a homogeneous model for convex optimization,
SIAM J. on Optim. 11(2):380-388, 2000
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E. D. Andersen and K. D. Andersen,
The MOSEK interior point optimizer for linear programming: an implementation of the homogeneous algorithm,
In High Performance Optimization:197--232,
H. Frenk, K. Roos, T. Terlaky and S. Zhang, editor(s),
Kluwer Academic Publishers
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E. D. Andersen,
On exploiting problem structure in a basis identification procedure for linear programming,
INFORMS Journal on Computing 11(1):95--103, 1999
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E. D. Andersen and Y. Ye,
On a homogeneous algorithm for the monotone complementarity problem,
Math. Programming 84(2):375--399, February 1999
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E. D. Andersen and Y. Ye,
A computational study of the homogeneous algorithm for large-scale convex optimization,
Computational Optimization and Applications 10:243--269, 1998
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E. D. Andersen and Y. Ye,
Combining interior-point and pivoting algorithms,
Management Sci. 42(12):1719--1731, December 1996
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K. D. Andersen,
A Modified Schur Complement Method for Handling Dense Columns in Interior-Point Methods for Linear Programming,
ACM Trans. Math. Software 22(3):348--356, 1996
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E. D. Andersen and K. D. Andersen,
Presolving in linear programming,
Math. Programming 71(2):221--245, 1995
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E. D. Andersen,
Finding all linearly dependent rows in large-scale linear programming,
Optimization Methods and Software 6:219--227, 1995