Results 11 to 20 of about 17,353,800 (271)
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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Journal of Computational and Applied Mathematics, 2000 The simplex method starts from a basic feasible solution and moves along the boundary of the feasible region until an optimum is reached. At each step, the algorithm brings only one new variable into the basic set, regardless of the total number of variables.
Potra, Florian A., Wright, Stephen J.
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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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Adapting the interior point method for the solution of linear programs on high performance computers [PDF]
, 1991 In this paper we describe a unified algorithmic framework for the interior point method (IPM) of solving Linear Programs (LPs) which allows us to adapt it over a range of high performance computer architectures. We set out the reasons as to why IPM makes
Levkovitz, R +5 more
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Sparse Approximations with Interior Point Methods [PDF]
SIAM Review, 2022 Large-scale optimization problems that seek sparse solutions have become ubiquitous. They are routinely solved with various specialized first-order methods. Although such methods are often fast, they usually struggle with not-so-well conditioned problems.
Valentina De Simone +4 more
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Experimental investigations in combining primal dual interior point method and simplex based LP solvers [PDF]
, 1993 The use of a primal dual interior point method (PD) based optimizer as a robust linear programming (LP) solver is now well established. Instead of replacing the sparse simplex algorithm (SSX), the PD is increasingly seen as complementing it. The progress
Levkovitz, R +5 more
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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.
Jurai Kardos +2 more
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Adapting the interior point method for the solution of LPs on serial, coarse grain parallel and massively parallel computers [PDF]
, 1990 In this paper we describe a unified scheme for implementing an interior point algorithm (IPM) over a range of computer architectures. In the inner iteration of the IPM a search direction is computed using Newton's method.
Levkovitz, R +3 more
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The Symbolic Interior Point Method
Proceedings of the AAAI Conference on Artificial Intelligence, 2017 Numerical optimization is arguably the most prominent computational framework in machine learning and AI. It can be seen as an assembly language for hard combinatorial problems ranging from classification and regression in learning, to computing optimal policies and equilibria in decision theory, to entropy minimization in information ...
Mladenov, Martin +2 more
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Convergence analysis of an Inexact Infeasible Interior Point method for Semidefinite Programming [PDF]
, 2004 In this paper we present an extension to SDP of the well known infeasible Interior Point method for linear programming of Kojima,Megiddo and Mizuno (A primal-dual infeasible-interior-point algorithm for Linear Programming, Math. Progr., 1993).
Pieraccini, Sandra +2 more
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