The Mosek Interior Point Optimizer for Linear Programming: An Implementation of the Homogeneous Algorithm

By Erling D. Andersen, Knud D. Andersen. 2000

835 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Control and Systems Engineering, Numerical Analysis, Optimization & Training

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Citations in the corpus

SciPy 1.0: fundamental algorithms for scientific computing in Python (2019, methodology): “Implementing the core algorithm of the commercial solver MOSEK 78 , it solves all of the 90 + NETLIB LP benchmark problems 79 tested.”
Optimal Transport for Domain Adaptation (2014, methodology): “with the MOSEK [2] linear programming solver2, whereas the other strategies follow our own implementation based on the Sinkhorn-Knopp method.”
On implementing a primal-dual interior-point method for conic quadratic optimization (2003, methodology): “The idea of centrality correctors can successfully be adapted to the case when the earlier presented homogeneous primal-dual algorithm is applied to a linear optimization problem[6].”
Robust Classification with Interval Data (2003, background): “For more on interiorpoint methods for convex optimization, we refer to [12, 1, 11], and the forthcoming excellent book [3].”
Knitro: An Integrated Package for Nonlinear Optimization (2006, methodology): “Mosek [1] is a primal-dual interior-point method for convex optimization, and Pennon [25] follows an augmented Lagrangian approach.”
Learning the Kernel Matrix with Semidefinite Programming (2002, methodology): “This QCQP problem is a special form of SDP (Boyd and Vandenberghe , 2001) which can be solved efficiently with programs such as SeDuMi (Sturm, 1999) or Mosek (Andersen and Andersen, 2000).”
ECOS: An SOCP solver for embedded systems (2013, background): “Methods for solving linear, quadratic, second-order cone or semi-definite programs (LPs, QPs, SOCPs, SDPs) are well understood, and many solver implementations have been developed and released, both in the public domain [5], [6] and as commercial codes [7], [8].”
Lower bound limit analysis of cohesive‐frictional materials using second‐order cone programming (2006, neutral): “In the case of MOSEK, for example, many aspects of the underlying algorithm have been studied and tested in detail, including: • use of a simple starting point that need not satisfy the equality constraints [38, 50]; • robust detection of infeasible problems [38]; • choice of the search direction an”
Transfusive image manipulation (2012, methodology): “We utilize the MOSEK solver [Andersen and Andersen 2000].”
Bound Tightening for the Alternating Current Optimal Power Flow Problem (2016, background): “The lower bound problem is a sparse lifted SDP relaxation that is strengthened with cuts and is solved with MOSEK [29].”
SciPy 1.0-Fundamental Algorithms for Scientific Computing in Python (2019, methodology): “Implementing the core algorithm of the commercial solver MOSEK 78 , it solves all of the 90 + NETLIB LP benchmark problems 79 tested.”
A Robust Minimax Approach to Classification (2002, background): “General-purpose programs such as SeDuMi (Sturm, 1999) or Mosek (Andersen and Andersen, 2000) can handle those problems efficiently.”
Fast online deconvolution of calcium imaging data (2016, background): “un time of our algorithm to a variety of state of the art convex solvers that can all be conveniently called from the convex optimization toolbox CVXPY [39]: embedded conic solver (ECOS, [40]), MOSEK [41], splitting conic solver (SCS, [42]) and GUROBI [43]. ECOS and MOSEK are the most competitive me”