A degenerate extreme point strategy for the classification of linear constraints as redundant or necessary

Caron, Richard J.; McDonald, J. F.; Ponic, C. M.

doi:10.1007/bf00941055

Cited by 70 publications

(61 citation statements)

References 11 publications

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“…Caron et.al [1] developed an algorithm for identifying the redundant constraint. In this method, the objective function of the original LPP is not considered.…”

Section: Redundant Removal Technique:-mentioning

confidence: 99%

Better Performance of Simplex Method on Transport Network With Non – Integer Edge Capacities.

Kalaiarasi¹,

raj²

2017

IJAR

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Operation Research problems (OR) have been solved by operation research technique efficiently for a long time. Graph theory techniques are competent with OR techniques in some area like transport problem. Identification of a better technique to solve the OR problem is very important. In this paper, the better performance of Big M method on transport network with non -integer edge capacities is reported. The redundant constraints removal in Big M method improve its performance. Graph theory is a very natural and powerful tool in operation research. The areas of OR in which graph theory is used most frequently and profitably are transport networks and theory of games In this paper, network -flow problems is formulated and solved using graph theory technique and operation research technique and the better performance is reported. The redundant constraints removal in OR technique improves its performance.

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“…Caron et.al [1] developed an algorithm for identifying the redundant constraint. In this method, the objective function of the original LPP is not considered.…”

Section: Redundant Removal Technique:-mentioning

confidence: 99%

Better Performance of Simplex Method on Transport Network With Non – Integer Edge Capacities.

Kalaiarasi¹,

raj²

2017

IJAR

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“…Several methods for classifying constraints exist. For example, there are deterministic algorithms [10,13], probabilistic hit-and-run methods [7], and a probabilistic method based on an equivalence between the constraint classification problem and the problem of finding a feasible solution to a set covering problem [9]. A survey and comparison of strategies for classifying constraints are given in [9,13].…”

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confidence: 99%

“…To classify constraints not detected by the projection method, we use another approach outlined in [10].…”

mentioning

confidence: 99%

“…We do so by applying the projection method to a linearization of the constraints, and we argue that it is less costly than applying the approach of [10].…”

mentioning

confidence: 99%

“…In the first part of the section, we introduce a definition of the ε-active constraints and discuss some scaling issues. The second part of Section 3 contains essential definitions and results on redundancy [10,13,19,25] that are required for our analysis. Then we propose our projection method to determine nonredundant constraints, and we briefly describe a more expensive follow-up approach to be applied if some constraints are not identified by the projection method.…”

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confidence: 99%

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Pattern Search Methods in the Presence of Degeneracy

Abramson¹,

Brezhneva²,

Dennis³

2003

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Abstract. This paper deals with generalized pattern search (GPS) algorithms for linearly constrained optimization. At each iteration, the GPS algorithm generates a set of directions that conforms to the geometry of any nearby linear constraints. This set is then used to construct trial points to be evaluated during the iteration. In previous work, Lewis and Torczon developed a scheme for computing the conforming directions, but it assumed no degeneracy near the current iterate. The contribution of this paper is to provide a detailed algorithm for constructing the set of directions whether or not the constraints are degenerate. One difficulty in the degenerate case is in classifying constraints as redundant and nonredundant. We give a short survey of the main definitions and methods for treating redundancy and propose an approach to identify nonredundant ε-active constraints, which may be useful for other active set algorithms. We also introduce a new approach for handling nonredundant linearly dependent constraints, which maintains GPS convergence properties without significantly increasing computational cost. Some simple numerical tests illustrate the effectiveness of the algorithm. We conclude by briefly considering the extension of our ideas to nonlinear constraints with linearly dependent constraint gradients.

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Computation of maximal output admissible sets for linear systems with polynomial constraints

et al. 2023

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In this technical note we study the computation of the Maximal Output Admissible Set for linear systems subject to polynomial constraints. The computation of an inner approximation of the Maximal Output Admissible Sets requires the determination of constraint redundancy. We use a procedure to determine polynomial constraint redundancy based on a consequence of Putinar's Positivstellensatz. Further, we present a modification of the algorithm to compute the Maximal Output Admissible Set with improved performance. Lastly, demonstrate the potential for practical applications in two case studies of spacecraft rendezvous and control of an electromagnetic actuator.

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A degenerate extreme point strategy for the classification of linear constraints as redundant or necessary

Cited by 70 publications

References 11 publications

Better Performance of Simplex Method on Transport Network With Non – Integer Edge Capacities.

Better Performance of Simplex Method on Transport Network With Non – Integer Edge Capacities.

Pattern Search Methods in the Presence of Degeneracy

Computation of maximal output admissible sets for linear systems with polynomial constraints

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