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An Interior-Point Method for Semidefinite Programming [PDF]
SIAM Journal on Optimization, 1996 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Christoph Helmberg +2 more
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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.
Nikolaos Ploskas, Nikolaos Samaras
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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.
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, 1992This 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), 1994In 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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On the Complexity of a Practical Interior-Point Method
SIAM Journal on Optimization, 1998Summary: The theory of self-concordance in convex optimization has been used to analyze the complexity of interior-point methods based on Newton's method. For large problems, it may be impractical to use Newton's method; here we analyze a truncated-Newton method, in which an approximation to the Newton search direction is used.
Stephen G. Nash, Ariela Sofer
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1996
Abstract The interest in interior point methods for linear programming emerged from Karmarkar’s contribution in 1984. This field has soon become one of the most active in the area of mathematical programming. It introduced new ideas and techniques that now have received their own place among the basic tools in optimization.
Cornelis Roos, Jean-Philippe Vial
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Abstract The interest in interior point methods for linear programming emerged from Karmarkar’s contribution in 1984. This field has soon become one of the most active in the area of mathematical programming. It introduced new ideas and techniques that now have received their own place among the basic tools in optimization.
Cornelis Roos, Jean-Philippe Vial
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Journal of Optimization Theory and Applications, 1998
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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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The Kantorovich Theorem and interior point methods
Mathematical Programming, 2004zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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