On the convergence of a generalized Reduced gradient algorithm for nonlinear programming problems

Schittkiowski, K.

doi:10.1080/02331938608843192

Cited by 3 publications

(2 citation statements)

References 19 publications

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“…The first recursive or sequential quadratic programming code is the subroutine NLPQL of Schittkowski (1985Schittkowski ( , 1986. Subproblems are 80lved by a dual algorithm based on a routine written by Powell (1983).…”

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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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confidence: 99%

Numerical comparison of nonlinear programming algorithms for structural optimization

Schittkowski

Zillober

Zotemantel³

1994

Structural Optimization

102

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“…The results are presented in Table 6 (Crisp Model and Rough Model by Hamzehee Method) and Table 7 (Rough Model by Expected Value Technique). The convergence of the GRG method is also well established (shown in Appendix A.5) [33]. To compare the results for existence of different constraints, we present the following Table 8 for η = 0.5.…”

Section: Numerical Experimentsmentioning

confidence: 93%

Constrained FC 4D MITPs for Damageable Substitutable and Complementary Items in Rough Environments

et al. 2019

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Very often items that are substitutable and complementary to each other are sent from suppliers to retailers for business. In this paper, for these types of items, fixed charge (FC) four-dimensional (4D) multi-item transportation problems (MITPs) are formulated with both space and budget constraints under crisp and rough environments. These items are damageable/breakable. The rates of damageability of the items depend on the quantity transported and the distance of travel i.e., path. A fixed charge is applied to each of the routes (independent of items). There are some depots/warehouses (origins) from which the items are transported to the sales counters (destinations) through different conveyances and routes. In proposed FC 4D-MITP models, per unit selling prices, per unit purchasing prices, per unit transportation expenditures, fixed charges, availabilities at the sources, demands at the destinations, conveyance capacities, total available space and budget are expressed by rough intervals, where the transported items are substitutable and complementary in nature. In this business, the demands for the items at the destinations are directly related to their substitutability and complementary natures and prices. The suggested rough model is converted into a deterministic one using lower and upper approximation intervals following Hamzehee et al. as well as Expected Value Techniques. The converted model is optimized through the Generalized Reduced Gradient (GRG) techniques using LINGO 14 software . Finally, numerical examples are presented to illustrate the preciseness of the proposed model. As particular cases, different models such as 2D, 3D FCMITPs for two substitute items, one item with its complement and two non substitute non complementary items are derived and results are presented.

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Convergence properties of a class of reduced gradient algorithms in linearly constrained minimization

Gaviano

1991

Optimization

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On the convergence of a generalized Reduced gradient algorithm for nonlinear programming problems

Cited by 3 publications

References 19 publications

Numerical comparison of nonlinear programming algorithms for structural optimization

Numerical comparison of nonlinear programming algorithms for structural optimization

Constrained FC 4D MITPs for Damageable Substitutable and Complementary Items in Rough Environments

Convergence properties of a class of reduced gradient algorithms in linearly constrained minimization

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