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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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Interior point stabilization for column generation
Operations Research Letters, 2007zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Rousseau, Louis-Martin +2 more
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Dual interior point algorithms
Russian Mathematics, 2011zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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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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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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Infeasible-Interior-Point Algorithms
1996An interior-point algorithm whose initial point is not restricted to a feasible point is called an infeasible-interior-point algorithm. The algorithm directly solves a given linear programming problem without using any artificial problem. So the algorithm has a big advantage of implementation over a feasible-interior-point algorithm, which has to start
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