A set of performance criteria for evaluating optimization software with regard to efficiency, reliability, and accuracy is presented. A numerical comparison of 5 constrained nonlinear programming codes is characteriz...
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A set of performance criteria for evaluating optimization software with regard to efficiency, reliability, and accuracy is presented. A numerical comparison of 5 constrained nonlinear programming codes is characterized, which is undertaken in order to test the usefulness and general applicability of the proposed performance criteria. The results of the numerical comparison are explored, and the proposed criteria are compared to the criteria traditionally used in comparative evaluations of nonlinear programming codes, with particular reference to machine dependence and the applicability to test problems with unknown solutions. A separate small-scale computational experiment is described that is undertaken specifically to test the machine dependence of the criteria. The deficiencies of the proposed new criteria are identified. For example, the operation and operand count required to determine the direct computational effort is tedious.
Due to their large variety of applications, complex optimization problems induced a great effort to develop efficient solution techniques, dealing with both continuous and discrete variables involved in nonlinear func...
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Due to their large variety of applications, complex optimization problems induced a great effort to develop efficient solution techniques, dealing with both continuous and discrete variables involved in nonlinear functions. But among the diversity of those optimization methods, the choice of the relevant technique for the treatment of a given problem keeps being a thorny issue. Within the process engineering context, batch plant design problems provide a good framework to test the performances of various optimization methods: on the one hand, two mathematical programming techniquesDICOPT++ and SBB, implemented in the GAMS environmentand on the other hand, one stochastic method, i.e., a genetic algorithm. Seven examples, showing an increasing complexity, were solved with these three techniques. The resulting comparison enables the evaluation of their efficiency in order to highlight the most appropriate method for a given problem instance. It was proved that the best performing method is SBB, even if the genetic algorithm (GA) also provides interesting solutions, in terms of quality as well as of computational time.
For a nonlinear programming problem with a canonical perturbations, we give an elementary proof of the following result: If the Karush-Kuhn-Tucker map is locally single-valued and Lipschitz continuous, then the linear...
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For a nonlinear programming problem with a canonical perturbations, we give an elementary proof of the following result: If the Karush-Kuhn-Tucker map is locally single-valued and Lipschitz continuous, then the linear independence condition for the gradients of the active constraints and the strong second-order sufficient optimality condition hold.
In this paper, we propose a novel multiattribute decision making (MADM) method using the nonlinear programming (NLP) methodology and the proposed score function of interval-valued intuitionistic fuzzy values (IVIFVs)....
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In this paper, we propose a novel multiattribute decision making (MADM) method using the nonlinear programming (NLP) methodology and the proposed score function of interval-valued intuitionistic fuzzy values (IVIFVs). Firstly, we propose a new score func-tion of IVIFVs to conquer the drawbacks of the existing score functions of IVIFVs. Then, we construct the converted matrix based on the proposed score function of IVIFVs by cal-culating the score value of each IVIFV in the decision matrix (DM) offered by the decision maker (DMK). Then, we construct the NLP model via the obtained converted matrix and the interval-valued intuitionistic fuzzy (IVIF) weight of each attribute given by the DMK. Then, we solve the NLP model to obtain the optimal weight for each attribute. Then, based on the obtained converted matrix and the obtained optimal weight of each attribute, we calculate the weighted score of each alternative. Finally, the alternatives are ranked on the basis of the obtained weighted scores of the alternatives. The larger the weighted score of an alter-native, the better the preference order of the alternative. The proposed MADM method can overcome the drawbacks of the existing MADM methods. It offers us a very useful approach for MADM in IVIF settings. (c) 2022 Elsevier Inc. All rights reserved.
An exact augmented Lagrangian function for the nonlinear nonconvex programming problems with inequality constraints was discussed. Under suitable hypotheses, the relationship was established between the local unconstr...
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An exact augmented Lagrangian function for the nonlinear nonconvex programming problems with inequality constraints was discussed. Under suitable hypotheses, the relationship was established between the local unconstrained minimizers of the augmented Lagrangian function on the space of problem variables and the local minimizers of the original constrained problem. Furthermore, under some assumptions, the relationship was also established between the global solutions of the augmented Lagrangian function on some compact subset of the space of problem variables and the global solutions of the constrained problem. Therefore, f^om the theoretical point of view, a solution of the inequality constrained problem and the corresponding values of the Lagrange multipliers can be found by the well-known method of multipliers which resort to the unconstrained minimization of the augmented Lagrangian function presented.
In this paper, a formulation of an interior-point Newton method for general nonlinear programming problems is presented. The formulation uses the Coleman-Li scaling matrix. The local convergence and the q-quadratic ra...
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In this paper, a formulation of an interior-point Newton method for general nonlinear programming problems is presented. The formulation uses the Coleman-Li scaling matrix. The local convergence and the q-quadratic rate of convergence for the method are established under the standard assumptions of the Newton method for general nonlinear programming.
In this paper, the goal is to incorporate qualitative criteria in addition to quantitative criteria to facility layout design (FLD) problem. To this end, we present an integrated methodology based on the synthetic val...
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In this paper, the goal is to incorporate qualitative criteria in addition to quantitative criteria to facility layout design (FLD) problem. To this end, we present an integrated methodology based on the synthetic value of fuzzy judgments and nonlinear programming (SVFJ-NLP). The facility layout patterns (FLPs) together with their performance measures of total cost of material handling are generated by a computer-aided layout-design tool, CRAFT. Also, the performance measures of second quantitative criterion (construction cost of width walls) are calculated by appraising these FLPs. The SVFJ is then applied to collect the performance measures related to qualitative criteria and finally, a non-linear programming (NLP) model is proposed to solve the FLD. Results obtained from a real case study validate the effectiveness of the proposed model. (C) 2011 Elsevier Ltd. All rights reserved.
In recent work, the local convergence behavior of path-following interior-point methods and sequential quadratic programming methods for nonlinear programming has been investigated for the case in which the assumption...
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In recent work, the local convergence behavior of path-following interior-point methods and sequential quadratic programming methods for nonlinear programming has been investigated for the case in which the assumption of linear independence of the active constraint gradients at the solution is replaced by the weaker Mangasarian-Fromovitz constraint qualification. In this paper, we describe a stabilization of the primal-dual interior-point approach that ensures rapid local convergence under these conditions without enforcing the usual centrality condition associated with path-following methods. The stabilization takes the form of perturbations to the coefficient matrix in the step equations that vanish as the iterates converge to the solution.
This study proposes a fuzzy and nonlinear programming approach for ubiquitous hotel recommendation. In the proposed approach, the weights of the attributes of a hotel differ among travelers, among locations, and over ...
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This study proposes a fuzzy and nonlinear programming approach for ubiquitous hotel recommendation. In the proposed approach, the weights of the attributes of a hotel differ among travelers, among locations, and over time. In addition, the weights assigned by a traveler are considered uncertain, and this uncertainty is resolved by defining these weights in fuzzy values. The overall performance of a hotel is then evaluated with the fuzzy weighted average of performance levels along all attribute dimensions. Subsequently, a nonlinear programming model is formulated and solved to derive the fuzzy values of weights that tailor the recommendation results to travelers' choices. The proposed fuzzy and nonlinear programming approach was applied to a small region in the Seatwen District, Taichung City, Taiwan, and it satisfactorily explained travelers' hotel choices in a ubiquitous environment.
Filter approaches, initially proposed by Fletcher and Leyffer in 2002, are recently attached importance to. If the objective function value or the constraint violation is reduced, this step is accepted by a filter, wh...
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Filter approaches, initially proposed by Fletcher and Leyffer in 2002, are recently attached importance to. If the objective function value or the constraint violation is reduced, this step is accepted by a filter, which is the basic idea of the filter. In this paper, the filter approach is employed in a sequential penalty quadratic programming (SlQP) algorithm which is similar to that of Yuan's. In every trial step, the step length is controlled by a trust region radius. In this work, our purpose is not to reduce the objective function and constraint violation. We reduce the degree of constraint violation and some function, and the function is closely related to the objective function. This algorithm requires neither Lagrangian multipliers nor the strong decrease condition. Meanwhile, in our SlQP filter there is no requirement of large penalty parameter. This method produces K-T points for the original problem. (c) 2005 Elsevier Ltd. All rights reserved.
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