The purpose of this study is to develop a crisp nonlinear method of programming to address production inventory problems based on both production inventory and conditions. In addition, we use a statistical confidence ...
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The purpose of this study is to develop a crisp nonlinear method of programming to address production inventory problems based on both production inventory and conditions. In addition, we use a statistical confidence interval to derive level (1-beta, 1-alpha) interval-valued fuzzy numbers, in order to solve problems in nonlinear programming for production inventory in the fuzzy sense.
In the present work, the optimal design of pre-fermentation and fermentation operations for ethanol production is obtained developing a superstructure mathematical model. Different configurations of both operations ar...
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In the present work, the optimal design of pre-fermentation and fermentation operations for ethanol production is obtained developing a superstructure mathematical model. Different configurations of both operations are simultaneously considered in an overall model which also includes detailed kinetics equations. The zero wait is the transfer policy selected for these stages for ensuring the quality of these operations, given the nature and characteristics of microbiological sugary substrates. From the overall proposed model, the optimal configuration of the stages, the number of duplicated units in each stage, the size of each process unit, the process variables as concentrations and flows, and the total investment and production cost are obtained. This model is formulated as a non-linear programming problem, which is solved by the Professional Software, General Algebraic Modeling System (GAMS) with the application of CONOPT solver. The optimal design and operation of pre-fermentation and fermentation stages are obtained and the attained results are compared with the structures in conventional distillery. (C) 2014 Elsevier Ltd. All rights reserved.
The purpose of this paper is to establish various converse duality results for nonlinear programming with cone constraints and its four dual models introduced by Chandra and Abha [S. Chandra, Abha, A note on pseudo-in...
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The purpose of this paper is to establish various converse duality results for nonlinear programming with cone constraints and its four dual models introduced by Chandra and Abha [S. Chandra, Abha, A note on pseudo-invex and duality in nonlinear programming, European Journal of Operational Research 122 (2000) 161-165]. (c) 2004 Published by Elsevier B.V.
Certain shortcomings are pointed out in the recent work of (S. Nanda, L.N. Das, European Journal of Operational Research 88 (1996) 572-577) and appropriate modifications are suggested for studying duality under pseudo...
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Certain shortcomings are pointed out in the recent work of (S. Nanda, L.N. Das, European Journal of Operational Research 88 (1996) 572-577) and appropriate modifications are suggested for studying duality under pseudo-invexity assumptions. (C) 2000 Elsevier Science B.V. All rights reserved.
A computational comparison of several recent semi-infinite nonlinear programming algorithms is presented. Because of the importance of this area, there have recently been proposed a number of algorithms having a globa...
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A computational comparison of several recent semi-infinite nonlinear programming algorithms is presented. Because of the importance of this area, there have recently been proposed a number of algorithms having a global convergence property. The algorithms used in this study include a feasible direction method and some variants of successive quadratic programming methods. Robustness and relative efficiency of the algorithms are examined on the basis of the results for some standard test examples chosen from earlier literature. [ABSTRACT FROM AUTHOR]
The objective of this paper is to conduct a theoretical study on the convergence properties of a second-order augmented Lagrangian method for solving nonlinear programming problems with both equality and inequality co...
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The objective of this paper is to conduct a theoretical study on the convergence properties of a second-order augmented Lagrangian method for solving nonlinear programming problems with both equality and inequality constraints. Specifically, we utilize a specially designed generalized Newton method to furnish the second-order iteration of the multipliers and show that when the linear independent constraint qualification and the strong second-order sufficient condition hold, the method employed in this paper is locally convergent and possesses a superlinear rate of convergence, although the penalty parameter is fixed and/or the strict complementarity fails.
Consideration is given to approximation programming method with gradually increasing/decreasing basis dimension. If the solution is found in the vertex of limiting polyhedron, i.e., on the boundary of intersection of ...
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The objective of this study was to compare the application of iterative linear programming (iteLP), sequential quadratic programming (SQP), and mixed integer nonlinear programming-based deterministic global optimizati...
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The objective of this study was to compare the application of iterative linear programming (iteLP), sequential quadratic programming (SQP), and mixed integer nonlinear programming-based deterministic global optimization (MINLP_DGO) on ration formulation for dairy cattle based on Nutrient Requirements of Dairy Cattle (NRC, 2001). Least-cost diets were formulated for lactating cows, dry cows, and heifers. Nutrient requirements including energy, protein, and minerals, along with other limitations on dry matter intake, neutral detergent fiber, and fat were considered as constraints. Five hundred simulations were conducted, with each simulation randomly selecting 3 roughages and 5 concentrates from the feed table in NRC (2001) as the feed resource for each of 3 animal groups. Among the 500 simulations for lactating cows, 57, 45, and 21 simulations did not yield a feasible solution when using iteLP, SQP, and MINLP_DGO, respectively. All the simulations for dry cows and heifers were feasible when using SQP and MINLP_DGO, but 49 and 11 infeasible simulations occurred when using iteLP for dry cows and heifers, respectively. The average ration costs per animal per day of the feasible solutions obtained by iteLP, SQP, and MINLP_DGO were $4.78 (+/- 0.71), $4.45 (+/- 0.65), and $4.44 (+/- 0.65) for lactating cows;$2.39 (+/- 0.52), $1.48 (+/- 0.26), and $1.48 (+/- 0.26) for dry cows;and $0.98 (+/- 0.72), $0.97 (+/- 0.15), and $0.91 (+/- 0.14) for heifers, respectively. The average computation time of iteLP, SQP, and MINLP_DGO were 0.59 (+/- 1.87) s, 1.15 (+/- 0.62) s, and 58.69 (+/- 68.45) s for lactating cows;0.041 (+/- 0.070) s, 0.76 (+/- 0.37) s, and 14.84 (+/- 39.09) s for dry cows;and 1.60 (+/- 2.90) s, 0.51 (+/- 0.19) s, and 16.45 (+/- 45.56) s for heifers, respectively. In conclusion, iteLP had limited capability of formulating least-cost diets when nonlinearity existed in the constraints. Both SQP and MINLP_DGO handled the nonlinear constraints well, with SQP being faster
Necessary optimality conditions for nonlinear programming are discussed in the present research. A new second-order condition is given, which depends oil a weak constant rank constraint requirement. We show that pract...
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Necessary optimality conditions for nonlinear programming are discussed in the present research. A new second-order condition is given, which depends oil a weak constant rank constraint requirement. We show that practical and publicly available algorithms (***/similar to egbirgiii/tango) of augmented Lagrangian type converge, after slight modifications, to stationary points defined by the new condition.
In this paper sufficient conditions for local and superlinear convergence to a Kuhn—Tucker point are established for a class of algorithms which may be broadly defined and comprise a quadratic programming algorithm f...
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In this paper sufficient conditions for local and superlinear convergence to a Kuhn—Tucker point are established for a class of algorithms which may be broadly defined and comprise a quadratic programming algorithm for repeated solution of a subproblem and a variable metric update to develop the Hessian in the subproblem. In particular the DFP update and an update attributed to Powell are shown to provide a superlinear convergent subclass of algorithms provided a start is made sufficiently close to the solution and the initial Hessian in the subproblem is sufficiently close to the Hessian of the Lagrangian at this point.
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