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  • 1
    Electronic Resource
    Electronic Resource
    s.l. : American Chemical Society
    Industrial and engineering chemistry 23 (1984), S. 522-528 
    Source: ACS Legacy Archives
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Type of Medium: Electronic Resource
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  • 2
    ISSN: 1436-4646
    Keywords: Geometric Programming ; Code Comparisons ; Numerical Testing ; Nonlinear Programming
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract Ten codes or code variants were used to solve the five equivalent posynomial GP problem formulations. Four of these codes were general NLP codes; six were specialized GP codes. A total of forty-two test problems was solved with up to twenty randomly generated starting points per problem. The convex primal formulation is shown to be intrinsically easiest to solve. The general purpose GRG code called OPT appears to be the most efficient code for GP problem solution. The reputed superiority of the specialized GP codes GGP and GPKTC appears to be largely due to the fact that these codes solve the convex primal formulation. The dual approaches are only likely to be competitive for small degree of difficulty, tightly constrained problems.
    Type of Medium: Electronic Resource
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  • 3
    Electronic Resource
    Electronic Resource
    Springer
    Journal of engineering mathematics 8 (1974), S. 311-314 
    ISSN: 1573-2703
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Technology
    Notes: Summary This paper demonstrates that the “equilibrium conditions” of generalized geometric programming can be interpreted as constrained derivatives of a transform of the dual program to the generalized geometric programming primal. Thus, iterative procedures employing these conditions amount to direct solution of the necessary conditions for a local minimum of the transformed dual expressed in constrained derivative form under the constraint qualification of nonsingularity and nondegeneracy.
    Type of Medium: Electronic Resource
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  • 4
    Electronic Resource
    Electronic Resource
    Springer
    Journal of optimization theory and applications 26 (1978), S. 185-203 
    ISSN: 1573-2878
    Keywords: Nonlinear programming ; geometric programming ; computation ; comparisons
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Numerous algorithms for the solution of geometric programs have been reported in the literature. Nearly all are based on the use of conventional programming techniques specialized to exploit the characteristic structure of either the primal or the dual or a transformed primal problem. This paper attempts to elucidate, via computational comparisons, whether a primal, a dual, or a transformed primal solution approach is to be preferred.
    Type of Medium: Electronic Resource
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  • 5
    Electronic Resource
    Electronic Resource
    Hoboken, NJ : Wiley-Blackwell
    AIChE Journal 21 (1975), S. 77-83 
    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: In most industrial applications the linear model used for optimization by linear programming involves significant uncertainties and inaccuracies in the model parameters. This paper presents a framework which allows uncertainties in the matrix elements of the linear program to be taken into account without requiring detailed knowledge of the statistical characterstics of these uncertainties. Three cases for the inequality constrained problem are considered: independent variations in the array elements, column dependent variations, and row dependent variations. In each case the problem can still be solved as a linear program. In the first two cases, the problem size is doubled, while for the row dependent case a finitely terminating cutting plane algorithm is constructed.
    Additional Material: 1 Tab.
    Type of Medium: Electronic Resource
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  • 6
    Electronic Resource
    Electronic Resource
    Hoboken, NJ : Wiley-Blackwell
    AIChE Journal 25 (1979), S. 220-229 
    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Flow sheet material balance calculations are greatly simplified if all process input streams, reaction stoichiometry, and conversions, as well as all stream and component split fractions, are specified. Yet in many applications, especially those arising in process design, the available material balance specifications can take on many alternate forms. Each of these additional specifications can readily be expressed as a linear or nonlinear constraint equation involving species or total flow rates.In this paper, an approach is developed for incorporating such specifications within the computational framework for solving unconstrained material balance problems. The linear as well as the nonlinear constraints are accommodated by generating a parametric solution to the underlying unconstrained problem. The parameters are determined by solving simultaneously first the linear and then the nonlinear constraint equations. Only as many equations are solved iteratively as there are nonlinear constraints.
    Additional Material: 2 Ill.
    Type of Medium: Electronic Resource
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  • 7
    Electronic Resource
    Electronic Resource
    Hoboken, NJ : Wiley-Blackwell
    AIChE Journal 26 (1980), S. 527-528 
    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Type of Medium: Electronic Resource
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  • 8
    Electronic Resource
    Electronic Resource
    Hoboken, NJ : Wiley-Blackwell
    AIChE Journal 21 (1975), S. 83-90 
    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: This paper presents a framework which allows uncertainties in the matrix elements of an equality constrained linear program to be taken into account without requiring detailed knowledge of the statical characteristics of these uncertainties. The results are derived using the model of the linear program with flexibility previously introduced for the inequality constrained case. However, because a feasible region common to all perturbed constraint sets does not exist in the equality constrained case, a flexibility set which intersects all perturbed sets individually rather than jointly is defined. The flexibility set is constructed by identifying a finite subset of all perturbed constraint sets which need to be investigated. Three cases for the equality constrained problem are considered: independent variations in the array elements, column dependent variations, and row dependent variations. In each case the problem is solved using a possibly large but decomposable linear program. In the first two cases, this program needs to be solved only once; while in the row dependent case an iterative but finite solution procedure is required.
    Additional Material: 1 Ill.
    Type of Medium: Electronic Resource
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  • 9
    Electronic Resource
    Electronic Resource
    Hoboken, NJ : Wiley-Blackwell
    AIChE Journal 25 (1979), S. 209-219 
    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: A study is made of the structure and properties of material balance simulation problems, and a technique is developed for their efficient solution. The method requires neither simultaneous solution of all balance equations nor iterative convergence methods. Instead, for each stream mixing point in the flow sheet, a vector balance equation is developed which contains as unknowns only mixer output streams. This unique set of vector equations is sequenced for solution by using precedence ordering and substitution techniques. It is shown that only as many vector equations need to be solved simultaneously as there are streams which would require iteration in the conventional sequential approach. Once the mixer output streams are calculated, the remaining intermediate process streams are evaluated directly with no further equation solving. Computational results are presented showing the efficiency of the method.
    Additional Material: 3 Ill.
    Type of Medium: Electronic Resource
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  • 10
    Electronic Resource
    Electronic Resource
    Hoboken, NJ : Wiley-Blackwell
    AIChE Journal 29 (1983), S. 820-829 
    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: The model described in Part I is applied to study an atmospheric fluidized-bed coal combustor. Extensive case studies are investigated on the effects of: enhanced grid region heat and mass transfer; bed void fraction; emulsion phase temperature; elutriation rates; reaction rate parameters; feed particle-size distribution; and particle superheat. Comparison is made with experimental results reported by Babcock and Wilcox. Proper representation of the grid region and use of actual feed distributions are shown to be essential to predicting combustor performance. Better particle elutriation and single-particle combustion submodels are found to be key requirements for improved combustor modeling.
    Additional Material: 6 Ill.
    Type of Medium: Electronic Resource
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