Results 231 to 240 of about 970,162 (282)
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2017
One of the most powerful methods for solving nonlinear optimization problems known as interior point methods is to be presented in this chapter. They are related to barrier functions. The terms “interior point methods” and “barrier methods” have the same significance and may be used interchangeably.
Richard W. Cottle, Mukund N. Thapa
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One of the most powerful methods for solving nonlinear optimization problems known as interior point methods is to be presented in this chapter. They are related to barrier functions. The terms “interior point methods” and “barrier methods” have the same significance and may be used interchangeably.
Richard W. Cottle, Mukund N. Thapa
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2008
Linear programs can be viewed in two somewhat complementary ways. They are, in one view, a class of continuous optimization problems each with continuous variables defined on a convex feasible region and with a continuous objective function. They are, therefore, a special case of the general form of problem considered in this text.
David G. Luenberger, Yinyu Ye
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Linear programs can be viewed in two somewhat complementary ways. They are, in one view, a class of continuous optimization problems each with continuous variables defined on a convex feasible region and with a continuous objective function. They are, therefore, a special case of the general form of problem considered in this text.
David G. Luenberger, Yinyu Ye
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Journal of Optimization Theory and Applications, 1998
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2013
The ellipsoid method has an undeniable historical relevance (due to its role in establishing polynomial time for linear programming with integer data). In addition, its underlying idea is simple and elegant. Unfortunately, it is not efficient in practice compared with both the simplex method and the more recent interior-point methods.
Peter Bürgisser, Felipe Cucker
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The ellipsoid method has an undeniable historical relevance (due to its role in establishing polynomial time for linear programming with integer data). In addition, its underlying idea is simple and elegant. Unfortunately, it is not efficient in practice compared with both the simplex method and the more recent interior-point methods.
Peter Bürgisser, Felipe Cucker
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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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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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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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