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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.
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2009
In a linear program, typically there are inequality constraints, and equality constraints, on the variables. In LP literature, a feasible solution is known as a:
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In a linear program, typically there are inequality constraints, and equality constraints, on the variables. In LP literature, a feasible solution is known as a:
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Interior Point Algorithms: Barrier Methods
1999In Chapter 7 the solution philosophy was based on an affine or projective transformation so that at the start of each iteration we were at the “center” of the polytope instead of on the boundary. This allowed a large step in the direction of a projected gradient.
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Polynomial-Time Interior-Point Methods
2018In this section, we present the problem classes and complexity bounds of polynomial-time interior-point methods. These methods are based on the notion of a self-concordant function. It appears that such a function can be easily minimized by the Newton’s Method.
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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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Interior Point Methods in Decomposition
1997Interior point techniques have not only shown their applicability in barrier methods for linear and nonlinear optimization, but also in cutting plane methods. Pioneers in this area are Goffin and Vial and co-workers (e.g., [74, 75, 77]). We briefly outline their approach.
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