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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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Linear and Nonlinear Programming, 2008
Linear programs can be viewed in two somewhat complementary ways. They are, in one view, a class of continuous optimization problems each with continuous variables defined on a convex feasible region and with a continuous objective function. They are, therefore, a special case of the general form of problem considered in this text.
David G. Luenberger, Yinyu Ye
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Linear programs can be viewed in two somewhat complementary ways. They are, in one view, a class of continuous optimization problems each with continuous variables defined on a convex feasible region and with a continuous objective function. They are, therefore, a special case of the general form of problem considered in this text.
David G. Luenberger, Yinyu Ye
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Primal-Dual Interior-Point Methods
Other Titles in Applied Mathematics, 1997Preface Notation 1. Introduction. Linear Programming Primal-Dual Methods The Central Path A Primal-Dual Framework Path-Following Methods Potential-Reduction Methods Infeasible Starting Points Superlinear Convergence Extensions Mehrotra's Predictor ...
Stephen J. Wright
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Quantum speedups for linear programming via interior point methods
SIAM journal on computing (Print), 2023We describe a quantum algorithm based on an interior point method for solving a linear program with $n$ inequality constraints on $d$ variables. The algorithm explicitly returns a feasible solution that is $\varepsilon$-close to optimal, and runs in time
Simon Apers, S. Gribling
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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
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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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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