Results 251 to 260 of about 2,434,105 (316)
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1996
It was mentioned earlier that the standard simplex method searches for an optimum to a linear program by moving along the surface of a convex polyhedron from one extreme point to an adjacent extreme point in a fashion such that the objective value is nondecreasing between successive basic feasible solutions.
Cornelis Roos, Jean-Philippe Vial
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It was mentioned earlier that the standard simplex method searches for an optimum to a linear program by moving along the surface of a convex polyhedron from one extreme point to an adjacent extreme point in a fashion such that the objective value is nondecreasing between successive basic feasible solutions.
Cornelis Roos, Jean-Philippe Vial
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Primal-Dual Interior-Point Methods for Domain-Driven Formulations
Mathematics of Operations Research, 2018We study infeasible-start primal-dual interior-point methods for convex optimization problems given in a typically natural form we denote as Domain-Driven formulation.
M. Karimi, L. Tunçel
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On the behavior of Lagrange multipliers in convex and nonconvex infeasible interior point methods
Mathematical programming, 2017We analyze sequences generated by interior point methods (IPMs) in convex and nonconvex settings. We prove that moving the primal feasibility at the same rate as the barrier parameter μ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage ...
G. Haeser, Oliver Hinder, Y. Ye
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2013
As was known, the simplex method moves on the underlying polyhedron, from vertex to adjacent vertex along descent edges, until an optimal vertex is reached, or unboundedness of the problem is detected. Nevertheless, it would go through an exponential number of vertices of the polyhedron (Sect. 3.8), and even stall at a vertex forever because of cycling
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As was known, the simplex method moves on the underlying polyhedron, from vertex to adjacent vertex along descent edges, until an optimal vertex is reached, or unboundedness of the problem is detected. Nevertheless, it would go through an exponential number of vertices of the polyhedron (Sect. 3.8), and even stall at a vertex forever because of cycling
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Accelerating Condensed Interior-Point Methods on SIMD/GPU Architectures
Journal of Optimization Theory and Applications, 2023F. Pacaud +4 more
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PARALLEL INEXACT NEWTON AND INTERIOR POINT METHODS
Parallel Computing, 2000An inexact Newton method is combined with a block iterative row-projection linear solver in order to solve sparse and large systems of nonlinear equations. It is underlined that a mutually orthogonal row-partition of the Jacobian matrix allows a simple solution of the linear least squares sub-problems.
BERGAMASCHI, LUCA, ZILLI, GIOVANNI
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Barrier Functions in Interior Point Methods
Mathematics of Operations Research, 1996We show that the universal barrier function of a convex cone introduced by Nesterov and Nemirovskii is the logarithm of the characteristic function of the cone. This interpretation demonstrates the invariance of the universal barrier under the automorphism group of the underlying cone.
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Interior Point Method: History and Prospects
Computational Mathematics and Mathematical Physics, 2019zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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2013
The same idea of the face method can be applied to the dual problem to derive a dual variant. The resulting method seems to be even more efficient than its primal counterpart.
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The same idea of the face method can be applied to the dual problem to derive a dual variant. The resulting method seems to be even more efficient than its primal counterpart.
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