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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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1995
In this chapter we will describe the methods that start with a point in the interior of the feasible region and continue through the interior towards the boundary solution. The study of these methods was started by the work of Karmarkar, and has been an area of intense international activity during the past decade.
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In this chapter we will describe the methods that start with a point in the interior of the feasible region and continue through the interior towards the boundary solution. The study of these methods was started by the work of Karmarkar, and has been an area of intense international activity during the past decade.
openaire +1 more source