Algorithmic Principles of Mathematical Programming

Faigle, Ulrich; Kern, Walter; Still, Georg J.

doi:10.1007/978-94-015-9896-5

Cited by 50 publications

(56 citation statements)

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“…The method applied to obtain the results presented in this paper is the Gauss-Newton technique. 25 Generally, choosing the model with the fewest parameters that can fully explain the behavior yields the most consistent results. If the response seems to rise in a first-order fashion to the steady state, then approximate model 2 is more appropriate.…”

Section: B Extraction Of Coating Propertiesmentioning

confidence: 99%

Sorption-induced static bending of microcantilevers coated with viscoelastic material

Wenzel

Josse

Heinrich

et al. 2008

Journal of Applied Physics

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Absorption of a chemical analyte into a polymer coating results in an expansion governed by the concentration and type of analyte that has diffused into the bulk of the coating. When the coating is attached to a microcantilever, this expansion results in bending of the device. Assuming that absorption ͑i.e., diffusion across the surface barrier into the bulk of the coating͒ is Fickian, with a rate of absorption that is proportional to the difference between the absorbed concentration and the equilibrium concentration, and the coating is elastic, the bending response of the coated device should exhibit a first-order behavior. However, for polymer coatings, complex behaviors exhibiting an overshoot that slowly decays to the steady-state value have been observed. A theoretical model of absorption-induced static bending of a microcantilever coated with a viscoelastic material is presented, starting from the general stress/strain relationship for a viscoelastic material. The model accounts for viscoelastic stress relaxation and possible coating plasticization. Calculated responses show that the model is capable of reproducing the same transient behavior exhibited in the experimental data. The theory presented can also be used for extracting viscoelastic properties of the coating from the measured bending data.

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Section: B Extraction Of Coating Propertiesmentioning

confidence: 99%

Sorption-induced static bending of microcantilevers coated with viscoelastic material

Wenzel

Josse

Heinrich

et al. 2008

Journal of Applied Physics

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“…(P) are given by the following: If x P is a local minimizer of problem (P), then there exist (see for example [2,5]) vectors 0 = λ ∈ R q+1 + and ν ∈ R m + satisfying q i=0 λ i ∇f i (x P ) + m k=1 ν k a k = 0, λ i f i (x P ) = 0, 1 ≤ i ≤ q and ν k (a k x P − b k ) = 0, 1 ≤ k ≤ m.…”

Section: The Fj and Kkt Conditions For Problems (P) And (Q)mentioning

confidence: 99%

“…For optimization problem (Q) the resulting FJ conditions are as follows: If x Q is a local minimizer of problem (Q), then there exist (see for example [2,5]…”

Section: The Fj and Kkt Conditions For Problems (P) And (Q)mentioning

confidence: 99%

An elementary proof of the Fritz-John and Karush–Kuhn–Tucker conditions in nonlinear programming

Birbil

Frenk

Still

2007

European Journal of Operational Research

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In this note we give an elementary proof of the Fritz-John and Karush-Kuhn-Tucker conditions for nonlinear finite dimensional programming problems with equality and/or inequality constraints. The proof avoids the implicit function theorem usually applied when dealing with equality constraints and uses a generalization of Farkas lemma and the Bolzano-Weierstrass property for compact sets. ABSTRACT. In this note we give an elementary proof of the Fritz-John and Karush-Kuhn-Tucker conditions for nonlinear finite dimensional programming problems with equality and/or inequality constraints. The proof avoids the implicit function theorem usually applied when dealing with equality constraints and uses a generalization of Farkas lemma and the Bolzano-Weierstrass property for compact sets.

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“…However, if the augmenting path is always selected according to the Edmonds-Karp rule ( [10]), i.e., as a path P ∈ P x with a minimal number of arcs, termination after at most |V | · |E| augmentations is guaranteed (see, e.g., [1] or [12]). So we find that the running time of the Ford-Fulkerson algorithm depends strongly on our preferences for breaking possible ties among augmenting paths.…”

Section: Introductionmentioning

confidence: 99%

Greedy Oriented Flows

2017

Self Cite

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We investigate the following greedy approach to attack linear programs of type max{1 T x | l ≤ Ax ≤ u} where A has entries in {−1, 0, 1}: The greedy algorithm starts with a feasible solution x and, iteratively, chooses an improving variable and raises it until some constraint becomes tight. In the special case, where A is the edgepath incidence matrix of some digraph G = (V, E), and l = 0, this greedy algorithm corresponds to the Ford-Fulkerson algorithm to solve the max (s, t)-flow problem in G w.r.t. edge-capacities u. It is well-known that the Ford-Fulkerson algorithm always terminates with an optimal flow, and that the number of augmentations strongly depends on the choice of paths in each iteration. The Edmonds-Karp rule that prefers paths with fewer arcs leads to a running time of at most |E| 2 augmentations. The paper investigates general types of matrices A and preference rules on the variables that make the greedy algorithm efficient. In this paper, we identify conditions that guarantee for the greedy algorithm not to cycle, and/or optimality of the greedy algorithm, and/or to yield a quadratic (in the number of rows) number of augmentations. We illustrate our approach with flow and circulation problems on regular oriented matroids.

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Algorithmic Principles of Mathematical Programming

Cited by 50 publications

References 0 publications

Sorption-induced static bending of microcantilevers coated with viscoelastic material

Sorption-induced static bending of microcantilevers coated with viscoelastic material

An elementary proof of the Fritz-John and Karush–Kuhn–Tucker conditions in nonlinear programming

Greedy Oriented Flows

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