Discretizing continuous attributes into a finite number of bins, can be considered as one of the key pre-processing steps to several machine learning tasks. The objective of this paper is to implement and analyze a di...
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In this paper, we propose a new multiattribute decision making (MADM) method based on the proposed score function (SF) of interval-valued intuitionistic fuzzy values (IVIFVs), the cosine similarity measure of IVIFVs, ...
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A system of differential equations is constructed to find Kuhn-Tucker points of a nonlinear programming problem with both equality and inequality constraints. It is proved that the Kuhn-Tucker point of the nonlinear p...
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A system of differential equations is constructed to find Kuhn-Tucker points of a nonlinear programming problem with both equality and inequality constraints. It is proved that the Kuhn-Tucker point of the nonlinear programming problem is an asymptotically stable equilibrium point of the differential system and a numerical algorithm is given based on the numerical integration of the proposed system of ordinary differential equations. The convergence theorem of the numerical algorithm is demonstrated. Several illustrative examples show the effectiveness of the algorithm.
This paper considers a multi-item inventory model with both production inventory and production conditions. We derive the crisp nonlinear programming model and use the statistical confidence interval to represent the ...
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This paper considers a multi-item inventory model with both production inventory and production conditions. We derive the crisp nonlinear programming model and use the statistical confidence interval to represent the demand quantity. We derive level (1-β, 1-α) fuzzy numbers and find nonlinear programming for production inventory in the fuzzy sense.
Convergence difficulties of nonlinear programming algorithms applied to control optimization are examined in this paper. It is shown that they are frequently due to the high dimensionality of the problem involved so t...
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Convergence difficulties of nonlinear programming algorithms applied to control optimization are examined in this paper. It is shown that they are frequently due to the high dimensionality of the problem involved so that they seem to be peculiar to control theory. Lack of convergence, convergence to a local minimum of the objective function and ill-posedness of the problem are examined and techniques to overcome these difficulties are proposed. In particular regularization procedures and separation of variables are examined to reduce the degree of ill-posedness and the number of local minima and a strategy to enhance convergence is discussed. A simple example from the chemical industry is examined.
The paper concerns the optimization methods, the structure and the functional characteristics of the optimization programming tools for nonlinear programming NP-16. The product is based chiefly on the achievements of ...
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The paper concerns the optimization methods, the structure and the functional characteristics of the optimization programming tools for nonlinear programming NP-16. The product is based chiefly on the achievements of the theory of nonlinear programming, and on the other hand, on the methods of developing interpreters and user-friendly interface. NP-16 solves the following problems: nonlinear problems of unconstrained optimization; nonlinear problems of constrained optimization; systems of nonlinear equations. For the purpose of facilitating the product operation and its building in into other software systems, the following modules have been developed: special screen editor for entering, editing and maintaining the description of the problem as a text file, visualization and storing of intermediate and final results; interpreter program for calculating the values of the nonlinear functions and constraints during the operation of the optimization modules; module for analytic obtaining of first derivatives. With its interpreter for calculating the nonlinear functions, NP-16 will suit users not experienced in programming languages. Experienced users, if they wish, can describe their problem using programming languages.
An efficient technique is suggested for the optimization of a function of many variables that is unimodal in the given domain of arguments. At the root of the technique is the iterative refining property of the approx...
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An efficient technique is suggested for the optimization of a function of many variables that is unimodal in the given domain of arguments. At the root of the technique is the iterative refining property of the approximation models of the function being optimized in approximation domains contracting to an extreme point.
In this paper, a class of augmented Lagrangiaus of Di Pillo and Grippo （DGALs） was considered, for solving equality-constrained problems via unconstrained minimization techniques. The relationship was further discus...
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In this paper, a class of augmented Lagrangiaus of Di Pillo and Grippo （DGALs） was considered, for solving equality-constrained problems via unconstrained minimization techniques. The relationship was further discussed between the uneonstrained minimizers of DGALs on the product space of problem variables and multipliers, and the solutions of the eonstrained problem and the corresponding values of the Lagrange multipliers. The resulting properties indicate more precisely that this class of DGALs is exact multiplier penalty functions. Therefore, a solution of the equslity-constralned problem and the corresponding values of the Lagrange multipliers can be found by performing a single unconstrained minimization of a DGAL on the product space of problem variables and multipliers.
An antisymmetrically laminated angle-ply plate is optimized with the objectives of minimizing the maximum dynamic deflection, maximizing the natural frequencies and/or maximizing the buckling load. The design variable...
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An antisymmetrically laminated angle-ply plate is optimized with the objectives of minimizing the maximum dynamic deflection, maximizing the natural frequencies and/or maximizing the buckling load. The design variables are the fiber orientation and the thickness of individual layers and are computed by using the methods of nonlinear programming. The concept of Pareto optimality is used in formulating the design problem and in reducing the multiple objectives into a single performance index. Numerical results are presented in the form of optimal tradeoff curves which allow the designer to assess the various possibilities open to him before deciding on a certain design. In this sense, the present design is an interactive process.
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