Results 21 to 30 of about 2,434,213 (315)
Log-Barrier Interior Point Methods Are Not Strongly Polynomial [PDF]
SIAM Journal on applied algebra and geometry, 2017 We prove that primal-dual log-barrier interior point methods are not strongly polynomial, by constructing a family of linear programs with $3r+1$ inequalities in dimension $2r$ for which the number of iterations performed is in $\Omega(2^r)$.
Xavier Allamigeon +3 more
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Quasi-Newton approaches to interior point methods for quadratic problems [PDF]
Computational optimization and applications, 2018 Interior point methods (IPM) rely on the Newton method for solving systems of nonlinear equations. Solving the linear systems which arise from this approach is the most computationally expensive task of an interior point iteration.
J. Gondzio, F. Sobral
semanticscholar +1 more source
Inversion of Gravity Anomalies Using Primal-Dual Interior Point Methods
AIMS Geosciences, 2016 Structural inversion of gravity datasets based on the use of density anomalies to derive robust images of the subsurface (delineating lithologies and their boundaries) constitutes a fundamental non-invasive tool for geological exploration.
Aaron A. Velasco, Azucena Zamora
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Journal of Numerical Analysis and Approximation Theory, 2023 Our aim in this work is to extend the primal-dual interior point method based on a kernel function for linear fractional problem. We apply the techniques of kernel function-based interior point methods to solve a standard linear fractional program.
Mousaab Bouafia, Adnan Yassine
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On the relationship of interior-point methods
International Journal of Mathematics and Mathematical Sciences, 1993 In this paper, we show that the moving directions of the primal-affine scaling method (with logarithmic barrier function), the dual-affine scaling method (with logarithmic barrier function), and the primal-dual interior point method are merely the Newton
Ruey-Lin Sheu, Shu-Cherng Fang
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A new search direction for full-Newton step infeasible interior-point method in linear optimization
Croatian Operational Research Review, 2023 In this work, we investigate a full Newton step infeasible interior-point method for linear optimization based on a new search direction which is obtained from an algebraic equivalent transformation of the central path system.
Behrouz Kheirfam
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Structure-Exploiting Interior Point Methods [PDF]
, 2020 Interior point methods are among the most popular techniques for large scale nonlinear optimization, owing to their intrinsic ability of scaling to arbitrary large problem sizes. Their efficiency has attracted in recent years a lot of attention due to increasing demand for large scale optimization in industry and engineering.
Kardoš, Juraj +2 more
openaire +2 more sources
Implementation of interior-point methods for LP based on Krylov subspace iterative solvers with inner-iteration preconditioning [PDF]
Computational optimization and applications, 2016 We apply novel inner-iteration preconditioned Krylov subspace methods to the interior-point algorithm for linear programming (LP). Inner-iteration preconditioners recently proposed by Morikuni and Hayami enable us to overcome the severe ill-conditioning ...
Yiran Cui +3 more
semanticscholar +1 more source
On the Turing Model Complexity of Interior Point Methods for Semidefinite Programming [PDF]
SIAM Journal on Optimization, 2015 It is known that one can solve semidefinite programs to within fixed accuracy in polynomial time using the ellipsoid method (under some assumptions). In this paper it is shown that the same holds true when one uses the short-step, primal interior point ...
E. Klerk, F. Vallentin
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Interior point methods in the year 2025
EURO Journal on Computational OptimizationInterior point methods (IPMs) have hugely influenced the field of optimization. Their fast development has been triggered by the seminal paper of Narendra Karmarkar published in 1984 which delivered a polynomial algorithm for linear programming and ...
Jacek Gondzio
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