Numerische Verfahren der nichtlinearen Optimierung

Spellucci, Peter

doi:10.1007/978-3-0348-7214-0

Cited by 123 publications

(51 citation statements)

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“…Stoer (1985) or Spellucci (1993) for a review]. Theoretical convergence has been investigated by Han (1976Han ( , 1977, Powell (1978aPowell ( , 1978b, Schittkowski (1983), for example, and the numerical comparative studies of Schittkowski (1980) and Hock and Schittkowski (1981) show their superiority over other mathematical programming algorithms under the above assumptions.…”

Section: Sequential Quadratic Programming Methodsmentioning

confidence: 99%

Numerical comparison of nonlinear programming algorithms for structural optimization

Schittkowski

Zillober

Zotemantel³

1994

Structural Optimization

102

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For FE-based structural optimiza.tion systems, a. large variety of different numerical algorithms ia ava.i\able, e.g. sequential linear programming, sequential quadratic programming, convex approximation, generalized reduced gradient, multiplier, penalty or optimality criteria. methods, and combina.tions of these approaches. The purpose of the pa.per is to present the numerical reaults of a comparative study of eleven rnathematical programrning codes which represent typical realizations of the mathema.tical methods mentioned. They a.re implemented in the structural optimization system MBB-LAGRANGE, which proceeds from a typical finite element analysis. The comparative results are obtained from a collection of79 test problems. The majority ofthem are academic test cases, the others possess some practical reßlliJe background. Optirnization is performed with respect to sizing of trusses and bearns, wall thicknesses, etc., subject to stress, displacement, and many other constraints. Numerical cornparison is based on reliability and efficiency measured by calculation time ana number of analyses needed to reach a certain accura.cy level.

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Section: Sequential Quadratic Programming Methodsmentioning

confidence: 99%

Numerical comparison of nonlinear programming algorithms for structural optimization

Schittkowski

Zillober

Zotemantel³

1994

Structural Optimization

102

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“…For an overview of these different optimization methods see, e.g. Mahnken [43], Bazaraa et al [5], Bertsekas [7], Luenberger [38], Dennis and Schnabel [14], Nocedal and Wright [58], Spellucci [71] and Powell [61]. The objective function (4.8) is, in general, non-convex which means that in addition to the global minimum local minima might occur.…”

Section: Solution Of the Inverse Problemmentioning

confidence: 99%

Generalized parameter identification for finite viscoelasticity

Kleuter

Menzel

Steinmann

2007

Computer Methods in Applied Mechanics and Engineering

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“…Consider the data points (1,20), (2,10), and (3,60). We first consider two approximations by a single number.…”

Section: Defining the Q-errormentioning

confidence: 99%

Preventing bad plans by bounding the impact of cardinality estimation errors

2009

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Query optimizers rely on accurate estimations of the sizes of intermediate results. Wrong size estimations can lead to overly expensive execution plans. We first define the q-error to measure deviations of size estimates from actual sizes. The q-error enables the derivation of two important results: (1) We provide bounds such that if the q-error is smaller than this bound, the query optimizer constructs an optimal plan. (2) If the q-error is bounded by a number q, we show that the cost of the produced plan is at most a factor of q 4 worse than the optimal plan. Motivated by these findings, we next show how to find the best approximation under the q-error. These techniques can then be used to build synopsis for size estimates. Finally, we give some experimental results where we apply the developed techniques.

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Numerische Verfahren der nichtlinearen Optimierung

Cited by 123 publications

References 0 publications

Numerical comparison of nonlinear programming algorithms for structural optimization

Numerical comparison of nonlinear programming algorithms for structural optimization

Generalized parameter identification for finite viscoelasticity

Preventing bad plans by bounding the impact of cardinality estimation errors

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