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Results 1 - 10
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326
A Primal-Dual Interior Point Method Whose Running Time Depends Only on the Constraint Matrix
, 1995
"... We propose a primal-dual "layered-step " interior point (LIP) algorithm for linear programming with data given by real numbers. This algorithm follows the central path, either with short steps or with a new type of step called a "layered least squares " (LLS) ste ..."
Abstract
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Cited by 57 (8 self)
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We propose a primal-dual "layered-step " interior point (LIP) algorithm for linear programming with data given by real numbers. This algorithm follows the central path, either with short steps or with a new type of step called a "layered least squares " (LLS
An Accelerated Interior Point Method Whose Running Time Depends Only on A
- IN PROCEEDINGS OF 26TH ANNUAL ACM SYMPOSIUM ON THE THEORY OF COMPUTING
, 1993
"... We propose a "layered-step" interior point (LIP) algorithm for linear programming. This algorithm follows the central path, either with short steps or with a new type of step called a "layered least squares" (LLS) step. The algorithm returns the exact global minimum after a finit ..."
Abstract
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Cited by 16 (2 self)
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We propose a "layered-step" interior point (LIP) algorithm for linear programming. This algorithm follows the central path, either with short steps or with a new type of step called a "layered least squares" (LLS) step. The algorithm returns the exact global minimum after a
A simplification to "A Primal-Dual Interior Point Method Whose Running Time Depends Only on the Constraint Matrix"
- In High performance optimization
, 1996
"... This note provides a simplified proof concerning the paper "A Primal-Dual Interior Point Method Whose Running Time Depends Only on the Constraint Matrix" by the same authors. In particular, we prove that Case II, one of the three cases in the method, can never occur. 1 Introduction Consid ..."
Abstract
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Cited by 2 (0 self)
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This note provides a simplified proof concerning the paper "A Primal-Dual Interior Point Method Whose Running Time Depends Only on the Constraint Matrix" by the same authors. In particular, we prove that Case II, one of the three cases in the method, can never occur. 1 Introduction
Probabilistic Analysis of Two Complexity Measures for Linear Programming Problems
- Math. Prog. A
, 1998
"... This note provides a probabilistic analysis of #A , a condition number used in the linear programming algorithm of Vavasis and Ye [14] whose running time depends only on the constraint matrix A # IR mn . We show that if A is a standard Gaussian matrix, then E(ln #A ) = O(min{m ln n, n}). Thus, the e ..."
Abstract
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Cited by 19 (3 self)
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This note provides a probabilistic analysis of #A , a condition number used in the linear programming algorithm of Vavasis and Ye [14] whose running time depends only on the constraint matrix A # IR mn . We show that if A is a standard Gaussian matrix, then E(ln #A ) = O(min{m ln n, n}). Thus
A Combinatorial Active Set Algorithm for Linear and Quadratic Programming, Under revision
, 2008
"... Abstract. We propose an algorithm for linear programming, which we call the Sequential Projection algorithm. This new approach is a primal improvement algorithm that keeps both a feasible point and an active set, which uniquely define an improving direction. Like the simplex method, the complexity o ..."
Abstract
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Cited by 3 (0 self)
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of our knowledge, this is the fastest known randomized algorithm for linear programming whose running time does not depend on the size of the numbers defining the problem instance. Many of our results generalize in a straightforward manner to mathematical programs that maximize a concave quadratic
ALGEBRAIC ALGORITHMS1
, 2012
"... This is a preliminary version of a Chapter on Algebraic Algorithms in the up- ..."
Abstract
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This is a preliminary version of a Chapter on Algebraic Algorithms in the up-
Approximating Covering Integer Programs with Multiplicity Constraints
- Discrete Appl. Math
, 2000
"... In a covering integer program (CIP), we seek an n-vector x of nonnegative integers, which minimizes c x; subject to Ax b; where all entries of A; b; c are nonnegative. In their most general form, CIPs include also multiplicity constraints of the type x d; i.e., arbitrarily large integers ar ..."
Abstract
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Cited by 11 (3 self)
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are not acceptable in the solution. The multiplicity constraints incur a dichotomy with respect to approximation between (0; 1)-CIPs whose matrix A contains only zeros and ones and the general case. Let m denote the number of rows of A: The well-known O(log m) costapproximation with respect to the optimum
ANY-TIME FUZZY CONTROLLER
, 2006
"... Fuzzy logic has been successfully applied in various fields. However, as fuzzy controllers increase in size and complexity, the number of control rules increases exponentially and real-time behavior becomes more difficult. This thesis introduces an any-time fuzzy controller. Much work has been done ..."
Abstract
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to optimize and speed up a controlling process, however none of the existing solutions provides an any-time behavior. This study first introduces several constraints that should be satisfied in order to guarantee an any-time behavior. These constraints are related to aggregation and defuzzification phases
Some Randomized Algorithms for Convex Quadratic Programming
"... Below we adapt some randomized algorithms of Welzl [10] and Clarkson [3] for linear programming to the framework of so--called LP--type problems. This framework is quite general and allows a unified and elegant presentation and analysis. LP--type problems include minimization of a convex quadratic f ..."
Abstract
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Cited by 2 (0 self)
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function subject to convex quadratic constraints as a special case, for which the above algorithms can be implemented efficiently. We show that the expected running times depend only linearly on the number of constraints, and illustrate this by some numerical results. Even though the framework of LP
Results 1 - 10
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326
