In this work, a kind of nonlinear programming problem with non-differential objective function and under the constraints expressed by a system of mixed fuzzy relation equations is investigated. First, some properties ...
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In this work, a kind of nonlinear programming problem with non-differential objective function and under the constraints expressed by a system of mixed fuzzy relation equations is investigated. First, some properties of this kind of optimization problem are obtained. Then, a polynomial-time algorithm for this kind of optimization problem is proposed based on these properties. Furthermore, we show that this algorithm is optimal for the considered optimization problem in this paper. Finally, numerical examples are provided to illustrate our algorithms.
Failure to satisfy Constraint Qualifications (CQs) leads to serious convergence difficulties for state-of-the-art nonlinear programming (NLP) solvers. Since this failure is often overlooked by practitioners, a strateg...
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Failure to satisfy Constraint Qualifications (CQs) leads to serious convergence difficulties for state-of-the-art nonlinear programming (NLP) solvers. Since this failure is often overlooked by practitioners, a strategy to enhance the robustness properties for problems without CQs is vital. Inspired by penalty merit functions and barrier-like strategies, we propose and implement a combination of both in Ipopt. This strategy has the advantage of consistently satisfying the Linear Independence Constraint Qualification (LICQ) for an augmented problem, readily enabling regular step computations within the interior-point framework. Additionally, an update rule inspired by the work of Byrd et al. (2012) is implemented, which provides a dynamic increase of the penalty parameter as stationary points are approached. Extensive test results show favorable performance and robustness increases for our ℓ 1 —penalty strategies, when compared to the regular version of Ipopt. Moreover, a dynamic optimization problem with nonsmooth dynamics formulated as a Mathematical Program with Complementarity Constraints (MPCC) was solved in a single optimization stage without additional reformulation. Thus, this ℓ 1 — strategy has proved useful for a broad class of degenerate NLPs.
Layout designing is one of the most useful research domains for improving the facility efficiency and human resources in organizations, since it composes the best layout designed by engineers to the organization by qu...
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Layout designing is one of the most useful research domains for improving the facility efficiency and human resources in organizations, since it composes the best layout designed by engineers to the organization by qualitative and quantitative criteria and choosing the best alternative. In this paper, a corrected non-linear programming method with Grey correlations has been used for choosing the best layout among the layouts produced by ALDEP software, because in choosing a layout design, several criteria with regard to the quality and quantity are simultaneously considered. The decision makers have to choose between Layout design alternatives and their choice have to consider all decision criteria. Wide range of approaches have been introduced to help decision makers this study presents an integrated model of Gray relation analysis and non-linear programming method and create some improvements on previous studies. By using the proposed method in this study, besides considering the variety of criteria, maximizing and minimizing the criteria has also been done simultaneously.
A theoretical framework based on a metric lattice is advanced which provides us with a systematic approach to the study of convergence properties of algorithms for solving multicriteria optimization problems in optima...
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A theoretical framework based on a metric lattice is advanced which provides us with a systematic approach to the study of convergence properties of algorithms for solving multicriteria optimization problems in optimal control and in nonlinear programming. The basic problem proposed is to find the set of noninferior (Pareto optimal) solution by numerical iterative methods. In the light of the framework advanced, several algorithms for multicriteria optimization problems which are versions of well known algorithms for scalar valued optimization problems in nonlinear programming and in optimal control can be devised naturally. A general global convergence theorem is proved which forms a basis to ensure algorithm convergence of a wide class of algorithms for multicriteria optimization problems.
Homotopy methods are powerful tools for solving nonlinear programming. Their global convergence can be generally established under conditions of the nonemptiness and boundness of the interior of the feasible set, the ...
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Homotopy methods are powerful tools for solving nonlinear programming. Their global convergence can be generally established under conditions of the nonemptiness and boundness of the interior of the feasible set, the Positive Linear Independent Constraint Qualification (PLICQ), which is equivalent to the Mangasarian-Fromovitz Constraint Qualification (MFCQ), and the normal cone condition. This paper provides a comparison of the existing normal cone conditions used in homotopy methods for solving inequality constrained nonlinear programming.
In this paper, a multi-objective nonlinear programming method is proposed. That is, the problems which have fuzzy multiple objective functions and constraints with GUB (Generalized Upper Bounding) structure are solved...
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In this paper, a multi-objective nonlinear programming method is proposed. That is, the problems which have fuzzy multiple objective functions and constraints with GUB (Generalized Upper Bounding) structure are solved by the proposed Hybridized Genetic Algorithms (HGA). This approach enables a flexible optimal system design by applying fuzzy goals and fuzzy constraints. In this Genetic Algorithm (GA), we propose a new chromosome representation that represents the GUB structure simply and effectively at the same time. Also, by introducing the HGAs that combine the proposed heuristic algorithm and makes use of the peculiarity of GUB structure to GA, the proposed approach is more efficient than the previous method in finding a solution. Further, to demonstrate the effectiveness of the proposed method, a large-scale optimal system reliability design problem is introduced.
To solve optimal control problems in which the state variables are of high dimension, the conventional numerical dynamic programming algorithm is in fact inapplicable owing to the well known difficulty in relation to ...
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To solve optimal control problems in which the state variables are of high dimension, the conventional numerical dynamic programming algorithm is in fact inapplicable owing to the well known difficulty in relation to the “ curse of dimensionality”. In this paper, a new technique called generalized time interval iteration algorithm is advanced which eliminates the difficulty of conventional dynamic programming thoroughly and can be applied to a fairly large class of optimal control problems of practical importance. The basic idea is to decompose the dynamic programming model into a series of nonlinear programming models with various scales in such a way to fit the structural feature of the problem in hand so as to reduce the total computation time. Hypotheses with rather mild conditions are proposed to guarantee the convergence of the algorithm. An important advantage of the technique proposed is that it is particularly suitable for parallel processing, and the total computation time can be reduced in a factor proportional to the number of time intervals provided that the quantity of the processors for parallel processing is enough.
Single-valued neutrosophic number (SVNN) is an appropriate extension of the ordinary fuzzy number. The key feature of the SVNN is that it can capture indeterminacy in the imprecise information. In real-life problems, ...
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General enough convergence conditions of the methods for conditional minimization problems solution are considered. The obtained conditions are necessary and sufficient conditions for some class of the sequential nonc...
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General enough convergence conditions of the methods for conditional minimization problems solution are considered. The obtained conditions are necessary and sufficient conditions for some class of the sequential nonconditional minimization methods. The conditions are generalized to the problems of multicriterion optimization. They have evident geometrical interpretation. Considered apparatus of convoluting functions allowed to construct a successful basis for the broad set of numerical methods of sequential nonconditional minimization in the form of a universal convoluting function. It led to development of simple dialogue means of flexible varying of ″fining hardness″ by different constraints in the considered optimization problem of metal-work parameters.
In a previous paper a unified outline of some of the most successful nonlinear programming methods was presented by the author, i.e. of penalty, multiplier, sequential quadratic programming, and generalized reduced gr...
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In a previous paper a unified outline of some of the most successful nonlinear programming methods was presented by the author, i.e. of penalty, multiplier, sequential quadratic programming, and generalized reduced gradient algorithms, to illustrate their common mathematical features and to explain the different numerical performance observed in practice. By defining a general algorithmic frame for all these approaches, a global convergence result can be achieved in the sense that starting from an arbitrary initial point, a stationary solution will be approximated.
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