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Interior-Point Methods

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.
Nikolaos Ploskas, Nikolaos Samaras
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Insights into the interior-point methods

ZOR Zeitschrift f�r Operations Research Methods and Models of Operations Research, 1992
This paper studies the search directions of three important interior- point algorithms, namely, the primal-affine scaling method, the dual- affine scaling method and the primal-dual interior point method (with logarithmic barrier function). From an algebraic point of view, the paper shows that the search directions of these three algorithms are merely ...
Ruey-Lin Sheu, Shu-Cherng Fang
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Interior point methods for placement

1994 IEEE International Symposium on Circuits and Systems (ISCAS), 1994
In VLSI layout optimization, the placement problem is usually solved with simulated annealing or heuristic algorithms. These procedures often begin with random initial configurations but may benefit greatly (in terms of execution time or quality of solution) when good initial relative placements are provided.
P. Chin, Anthony Vannelli
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Interior Point Methods

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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Interior-Point Methods

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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Inexact Interior-Point Method

Journal of Optimization Theory and Applications, 1998
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Barrier Functions in Interior Point Methods

Mathematics of Operations Research, 1996
We 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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