Purpose In this work, a numerical algorithm is presented for stability analysis of cold-formed steel (CFS) channel sections. Design/methodology/approach A nonlinear optimization problem is formulated using energy-base...
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Purpose In this work, a numerical algorithm is presented for stability analysis of cold-formed steel (CFS) channel sections. Design/methodology/approach A nonlinear optimization problem is formulated using energy-based technique of idealized channel section subject shear, compression and biaxial bending. The total potential energy is minimized with respect to skew angle and half wavelength of the buckling mode. The optimization algorithm is updated sequentially using quadratic approximation until minimum buckling coefficient is attained. The developed algorithm is validated using other numerical techniques. Findings The described algorithm is computationally effective and can be utilized in the industry for analysis of CFS channels under any load combination. Practical implications The paper offers a new tool for engineers in practice to analyze channels subject to combined loadings. Originality/value Very limited literature dealt with the stability of channels under combined loading. A new numerical algorithm is provided to practitioners to utilize in the industry for analysis of channel sections under combined loading. Unlike finite element or finite strip methods, the channel is not discretized into subelements. mathematical programming technique is used to find the buckling load. Parametric studies are then carried out to highlight influences of geometric interaction of the channel components and to provide useful guidance to the design of CFS channels.
This,study examines the impact that the size of the classification gap can have on the classificatory performance of a mathematical programming based discriminant model. In mathematical programming based models that p...
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This,study examines the impact that the size of the classification gap can have on the classificatory performance of a mathematical programming based discriminant model. In mathematical programming based models that project the discriminant scores onto a line, the discriminant score of an observation may fall into the gap between adjacent group intervals;thus there is no clear cut way to determine the group in which the observation should be classified. We examine a procedure that we refer to as the split gap approach. The split gap approach is defined as a strategy of estimating the performance of a mathematical programming based model using a nonzero gap size to separate group intervals and then splitting the gap between adjacent group intervals to classify future observations. Studies that propose models with a classification gap generally do not assess the effect of the gap on the performance of the model. This paper investigates this effect. A theoretical assessment and a Monte Carlo simulation are used to determine the impact of different gap sizes on a mixed integer programming model using a single function classification model for the three-group case.
mathematical programming approaches to the statistical classification problem have attracted considerable research interest since the early 1980s. In this paper a mixed-integer programming model is proposed for the mi...
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mathematical programming approaches to the statistical classification problem have attracted considerable research interest since the early 1980s. In this paper a mixed-integer programming model is proposed for the minimization of misclassification costs in the three-group problem. In the proposed model, distinct costs c(h \ g) can be assigned to the misclassification of an observation from one group to either of the other two groups. The standard parametric classification procedures (Fisher's linear discriminant function and Smith's quadratic discriminant function), as incorporated in commonly used statistical packages like SAS, SPSS and MINITAB, do not allow the assignment of distinct costs c(h \ g), when the number of groups is three or more. Using MBA admissions data, it is shown that the proposed model may be useful in assisting an academic institution in its screening of MBA applications, once the relative costs of erroneous admission decisions are assessed. (C) 2001 Elsevier Science Ltd. All rights reserved.
The development of new techniques for solving mathematical programming problems has accelerated, thus making choices among available options more complex. Experiment-design procedures, which can be used in testing ma...
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The development of new techniques for solving mathematical programming problems has accelerated, thus making choices among available options more complex. Experiment-design procedures, which can be used in testing mathematical programming software, are determined. Results of a test case using 4 codes that determine the best L1 approximation to a continuous linear function are given. The experiment makes use of 320 test problems created by a test problem generator, and several performance measures describe solution quality as well as computational effort. Results clearly indicate that solution quality is improved substantially by a final (double-precision) reinversion of the optimal basis matrix. Results of the investigation, however, are valid only for the specific type of problem described.
This article is devoted to the study of mathematical programming problems with vanishing constraints on Hadamard manifolds (in short, MPVC-HM). We present the Abadie constraint qualification (in short, ACQ) and (MPVC-...
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This article is devoted to the study of mathematical programming problems with vanishing constraints on Hadamard manifolds (in short, MPVC-HM). We present the Abadie constraint qualification (in short, ACQ) and (MPVC-HM)-tailored ACQ for MPVC-HM and provide some necessary conditions for the satisfaction of ACQ for MPVC-HM. Moreover, we demonstrate that the Guignard constraint qualification (in short, GCQ) is satisfied for MPVC-HM under certain mild restrictions. We introduce several (MPVC-HM)-tailored constraint qualifications in the framework of Hadamard manifolds that ensure satisfaction of GCQ. Moreover, we refine our analysis and present some modified sufficient conditions which guarantee that GCQ is satisfied. Several non-trivial examples are incorporated to illustrate the significance of the derived results. To the best of our knowledge, constraint qualifications for mathematical programming problems with vanishing constraints in manifold setting have not been explored before.
This paper introduces a mathematical programming model that overcomes the major methodological problem of a large ranking task: respondent fatigue and deteriorated decision quality caused by an excessive number of obj...
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This paper introduces a mathematical programming model that overcomes the major methodological problem of a large ranking task: respondent fatigue and deteriorated decision quality caused by an excessive number of objects to be ranked. The model was applied to the problem of ranking Marketing and International Business journals. There are more than 200 such journals, making direct ranking or rating very difficult, if not impossible. The result shows that the mathematical programming model uses very little information and yet can produce rankings that are in agreement with results obtained from direct ranking studies.
Proportional integral derivative (PID) controllers are extensively used in the process industry. As a result a large number of general purpose tuning methodologies are available. These tuning methodologies can offer i...
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Proportional integral derivative (PID) controllers are extensively used in the process industry. As a result a large number of general purpose tuning methodologies are available. These tuning methodologies can offer initial estimates of the parameters of the PID controllers. However, the design objectives used for the development of these tuning methods can be quite different from the performance objectives specific to a process under investigation. As a result, the control engineer often needs customized tuning methods in order to speed up or even eliminate the retuning procedure, and thus, minimize the time and effort needed to design a satisfactory closed loop system. This paper presents a general mathematical programming formulation for the development of customized PID controller tunings. A reformulation of the mathematical formulation is proposed that transforms the initially nonlinear formulation to a linear one that can be solved to global optimality. A number of case studies are presented to clarify the proposed methodology. (C) 2004 Elsevier B.V. All rights reserved.
作者：
Shapiro, JFMIT
Alfred P Sloan Sch Management Cambridge MA 02142 USA
This paper examines connections between data-driven models for analyzing a firm's strategic plans, which use activity-based costing and mathematical programming, and the resource-based view of the firm. After brie...
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This paper examines connections between data-driven models for analyzing a firm's strategic plans, which use activity-based costing and mathematical programming, and the resource-based view of the firm. After brief reviews of the three disciplines, extensions of activity-based costing methods to mathematical programming models for strategic resource planning are discussed. Applications of these models to supply chain planning in a multi-national food manufacturer, a specialty chemicals company, and a wholesaling/retailing company are presented. The paper concludes by using concepts from the resource-based view of the firm to interpret optimal solutions from mathematical programming models. Extensions to strategic planning under uncertainty using stochastic programming are also discussed briefly. (C) 1999 Elsevier Science B.V. All rights reserved.
In this paper, mathematical programming Technique is employed for stability analysis of multi-stiffened plates under combined in-plane loadings. As a first stage, a literature review for the numerical methods used for...
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In this paper, mathematical programming Technique is employed for stability analysis of multi-stiffened plates under combined in-plane loadings. As a first stage, a literature review for the numerical methods used for the analysis of the structure is presented. The mathematical formulation of the problem is then shown. Accuracy of the numerical algorithm is then checked with the solutions of other numerical techniques like Finite Element and Finite Strip Methods. Results are then presented illustrating the behaviour of the structure. The transition from the various buckling modes by changing the plate/stiffener proportions for various stiffening configurations is shown. Also, the influence of the stiffener spacing for plates under pure in-plane bending on the buckling behaviour of the plate is shown. Finally, efficiency of the described algorithm is compared with other numerical methods that are commonly used for stability analysis of multi-stiffened plates.
Discrete-time optimal control problems arise naturally in many economic problems. Despite the rapid growth in computing power and new developments in the literature, many economic problems are still quite challenging ...
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Discrete-time optimal control problems arise naturally in many economic problems. Despite the rapid growth in computing power and new developments in the literature, many economic problems are still quite challenging to solve. Economists are aware of the limitations of some of these approaches for solving these problems due to memory and computational requirements. However, many of the economic models present some special structure that can be exploited in an efficient manner. This paper introduces a decomposition methodology, based on a mathematical programming framework, to compute the equilibrium path in dynamic models by breaking the problem into a set of smaller independent subproblems. We study the performance of the method solving a set of dynamic stochastic economic models. The numerical results reveal that the proposed methodology is efficient in terms of computing time and accuracy. (C) 2006 Elsevier Ltd. All rights reserved.
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