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Ragnar Frisch and interior-point methods
Optimization Letters, 2014zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Olav Bjerkholt, Sjur Didrik Flåm
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The interior-point method for linear programming
IEEE Software, 1992A robust, reliable, and efficient implementation of the primal-dual interior-point method for linear programs, which is based on three well-established optimization algorithms, is presented. The authors discuss the theoretical foundation for interior-point methods which consists of three crucial building blocks: Newton's method for solving nonlinear ...
Greg Astfalk +3 more
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The Kantorovich Theorem and interior point methods
Mathematical Programming, 2004zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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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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On Numerical Issues of Interior Point Methods
SIAM Journal on Matrix Analysis and Applications, 2008This paper concerns some numerical stability issues of factorizations in interior point methods. In our investigation we focus on regularization techniques for the augmented system. We derive the fundamental property of regularization and necessary conditions for the convergence of iterative refinement. A relaxation technique is described that improves
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Interior point methods for equilibrium problems
Computational Optimization and Applications, 2011zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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An interior point method for nonlinear programming
Zeitschrift für Operations Research, 1979In this paper an interior point method is presented for nonlinear programming problems with inequality constraints. On defining a modified distance function the original problem is solved sequentially by using a method of feasible directions. At each iteration a usable feasible direction can be determined explicitly. Under certain assumptions it can be
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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.
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A Gravitational Interior Point Method for LP
OPSEARCH, 2005zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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In this paper we discuss the main concepts of structural optimization, a field of nonlinear programming, which was formed by the intensive development of modern interior-point schemes..
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