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Best proximity point theorems: exposition of a significant non-linear programming problem

JOURNAL OF GLOBAL OPTIMIZATION 2013年第4期56卷 1699-1705页

作者： Basha, S. Sadiq Shahzad, N. Jeyaraj, R. Anna Univ Dept Math Madras 600025 Tamil Nadu India King Abdulaziz Univ Dept Math Jeddah 21589 Saudi Arabia St Josephs Coll Higher Secondary Sch Tiruchirappalli 620002 India

The primary goal of this work is to address the non-linear programming problem of globally minimizing the real valued function x -> d(x, Tx) where T is presumed to be a non-self mapping that is a generalized proximal contraction in the setting of a metric space. Indeed, an iterative algorithm is presented to determine a solution of the preceding non-linear programming problem that focuses on global optimization. As a sequel, one can compute optimal approximate solutions to some fixed point equations and optimal solutions to some unconstrained non-linear programming problems.

关键词： Global optimization non-linear programming problem Best proximity point Optimal approximate solution Generalized proximal contraction Proximal contraction Fixed point

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Best proximity point theorems: exposition of a significant non-linear programming problem

Best proximity point theorems: exposition of a significant n...

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8th International Tri-Annual Conference on Optimization - Techniques and Applications (ICOTA)

关键词： Global optimization non-linear programming problem Best proximity point Optimal approximate solution Generalized proximal contraction Proximal contraction Fixed point

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A nonlinear programming approach to solve MADM problem with triangular fuzzy preference and non-preference information

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OPTIMIZATION AND ENGINEERING 2021年第2期22卷 1091-1116页

作者： Mehlawat, Mukesh Kumar Gupta, Pankaj Ahemad, Faizan Univ Delhi Dept Operat Res Delhi 110007 India

In this paper, we present a new approach to solve multi-attribute decision making (MADM) problems considering subjective preferences and non-preferences of the decision maker in the form of triangular fuzzy preference relations and triangular fuzzy non-preference relations, respectively. Some important characteristics of these relations are used to form non-linear programming problems corresponding to lower, middle, and upper limits of the triangular fuzzy numbers. The optimization problems corresponding to lower and upper limits are solved to obtain corresponding limits of basic triangular fuzzy multiplicative preference weights (TFMPWs) and basic triangular fuzzy multiplicative non-preference weights (TFMNPWs). The obtained optimal weight values are used to find the modal values of TFMPWs and TFMNPWs that helps in the ranking of the alternatives. The working of the proposed approach is demonstrated by solving a MADM problem from the literature. Furthermore, to validate the superiority of the proposed approach, a comparative analysis with similar existing approaches has been provided. The obtained results reveal the applicability and usefulness of the proposed approach.

关键词： non-linear programming problem Multi-attribute decision making Triangular fuzzy preference and non-preference relations Triangular fuzzy multiplicative weights Triangular intuitionistic fuzzy numbers

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A method to solve Pythagorean fuzzy transportation problems

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INTERNATIONAL JOURNAL OF SYSTEM ASSURANCE ENGINEERING AND MANAGEMENT 2023年第5期14卷 1847-1854页

作者： Bhatia, Tanveen Kaur Kumar, Amit Appadoo, S. S. Sharma, M. K. Thapar Inst Engn & Technol Sch Math Patiala 147004 Punjab India Univ Manitoba Asper Sch Business Dept Supply Chain Management Winnipeg MB Canada

Nagar et al. (Int J Syst Assur Eng Manag (2021). https://***/10.1007/s13198-021-01339-w) proposed a method to solve Pythagorean fuzzy transportation problems (transportation problems in which the unit transportation cost for supplying the product from a source to a destination is represented by a Pythagorean fuzzy number. Whereas, all other parameters are represented by a non-negative real number). Nagar et al. also claimed that their proposed method is more efficient as compared to the existing methods (Complex Intell Syst (2019) 5: 255-263, Adalya J (2020) 9(1): 1301-1308). In this paper, it is pointed out that in all these existing methods, some mathematical incorrect assumptions are considered. Therefore, it is inappropriate to use these existing methods to solve Pythagorean fuzzy transportation problems. To resolve the inappropriateness of these existing methods, a new method (named as Mehar method) is proposed to solve Pythagorean fuzzy transportation problems.

关键词： Pythagorean fuzzy numbers Pythagorean fuzzy transportation problem (PyFTP) Crisp transportation problem (CTP) non-linear programming problem

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Using a Direct Multiple Shooting Method to Control a Quadrotor 8

Using a Direct Multiple Shooting Method to Control a Quadrot...

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8th International Conference on Control, Decision and Information Technologies (CoDIT)

作者： Louadj, Kahina Marthon, Philippe Papaix, Philippe Lab Concept & Conduite Syst Prod UMMTO Tizi Ouzou Algeria Fed Univ Toulouse Midi Pyrenees Toulouse Res Inst Comp Sci ENSEEIHT Site Toulouse France Akli Mohand Oulhadj Univ Bouira Algeria

ISBN: (纸本)9781665496070

A direct multiple shooting method is considered to solve optimal control problems. The direct multiple shooting method is a numerical method for the solution of boundary value problems. The method divides the interval over which a solution is sought into several smaller intervals, solves an initial value problem in each of the smaller intervals, and imposes additional matching conditions to form a solution on the whole interval. This method transforms an optimal control problem into a non-linear programming problem. To solve this last problem, the zeros of the Jacobian of Lagrangian are computed by using the Newton's method. Then, this method is illustrated by a numerical example and finally, applied to control a quadrotor to minimize energy.

关键词： Optimal control Multiple Shooting Method non-linear programming problem Newton's method Quadrotor

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Fuzzy linear programming problem with fuzzy decision variables: A geometrical approach

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JOURNAL OF STATISTICS & MANAGEMENT SYSTEMS 2021年第4期24卷 853-863页

作者： Tadesse, Admasu Acharya, M. M. Sahoo, Manoranjan Acharya, Srikumar KIIT Univ Sch Appl Sci Dept Math Bhubaneswar 751024 Odisha India

Decision making problems force the decision maker to consider fuzzy decision variables in a fuzzy linear programming problem. Therefore, the proposed fuzzy linear programming problem considers a triangular fuzzy decision variable with triangular fuzzy parameters. A defuzzyfication method based on incenter of a triangle, which is formed by joining the vertices of the triangular fuzzy parameters and fuzzy decision variables. The coordinate of the incenter is obtained by using the concept of geometry. In next step, the incenter is considered as a vector quantity. Using the concept of obtaining the magnitude of a vector, the final mathematical model is formulated. The final mathematical programming problem is a crisp non-linear programming problem. The resultant crisp mathematical programming problem is solved by appropriate mathematical software. A numerical example is presented to illustrate the methodology.

关键词： Triangular fuzzy number Fuzzy decision variable non-linear programming problem

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Decomposition of parametric space for bi-objective optimization problem using neural network approach

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OPSEARCH 2018年第2期55卷 502-531页

作者： Abo-Sinna, Mahmoud A. Rizk-Allah, Rizk M. Menoufia Univ Dept Basic Engn Sci Fac Engn Shibin Al Kawm Egypt

A new gradient-based neural network approach is proposed for solving nonlinear programming problems (NLPPs) and bi-objective optimization problems (BOOPs). The most prominent feature of the proposed approach is that it can converge rapidly to the equilibrium point (optimal solution), for an arbitrary initial point. The proposed approach is affirmed to be stable in the sense of Lyapunov and it is capable for obtaining the optimal solution in solving both NLPPs and BOOPs tasks. Further, BOOP is converted into an equivalent optimization problem by the mean of the weighted sum method, where the Pareto optimal solutions are obtained by using different weights. Also the decomposition of parametric space for BOOP is analyzed in details based on the stability set of the first kind. The experiments results also affirmed that the proposed approach is a promising approach and has an effective performance.

关键词： Bi-objective optimization problem Neural networks non-linear programming problem Pareto-optimal solutions Asymptotic stability

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Selective Maintenance Model for Modular System 13

Selective Maintenance Model for Modular System

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IEEE International Conference on Mechatronics and Automation

作者： Hou, Jinxin Qian, Yanling Natl Univ Def Technol Coll Informat Syst & Management Changsha Hunan Peoples R China Natl Univ Def Technol Lab Sci & Technol Integrated Logist Support Changsha Hunan Peoples R China

ISBN: (纸本)9781509023967

In many situations, systems are required to perform maintenance actions at the planned down time. Because of the limitation of down time, it is often impossible to perform maintenance action for all components in system. Therefore, the maintenance manager should make a decision to choose part of the components to be maintained in the limited down time. This problem is called selective maintenance. In this paper, we provide a selective maintenance model for modular system. We formulate the selective maintenance model as a non-linear programming problem. The maximum reliability gained by maintaining the modular system is formulated as objective. And we show the effectiveness of the proposed model via a numerical example.

关键词： selective maintenance modular system non-linear programming problem reliability

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Best proximity point theorems: unriddling a special nonlinear programming problem

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TOP 2014年第2期22卷 543-553页

作者： Basha, S. Sadiq Anna Univ Dept Math Madras 600025 Tamil Nadu India

This paper addresses the non-linear programming problem of globally minimizing the real valued function x -> d(x,Sx) where S is a generalized proximal contraction in the setting of a metric space. Eventually, one c... 详细信息

关键词： Global optimization non-linear programming problem Optimal approximate solution Best proximity point Fixed point Proximal contraction Generalized proximal contraction Proximal cyclic contraction Generalized proximal cyclic contraction

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Ascent trajectory planning on-board based on direct optimisation method

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INTERNATIONAL JOURNAL OF MODELLING IDENTIFICATION AND CONTROL 2013年第4期19卷 388-395页

作者： Lu, Xuefang Wang, Yongji Huazhong Univ Sci & Technol Dept Control Sci & Engn Key Lab Minist Educ Image Proc & Intelligent Control Wuhan Hubei Peoples R China

In this paper, an on-board trajectory planning algorithm is proposed for atmospheric ascent. To deal with the impact of disturbance, the on-board trajectory planning algorithm updates the reference trajectory by solving an optimal control problem on-board. Considering the strong non-linear aerodynamic, the optimal control problem is transformed into non-linear programming problem by trajectory discretisation. The direct optimisation method is implemented for this non-linear programming problem. Due to the small amount of discrete nodes and the initial guess solution which is close to the optimisation solution, the direct optimisation method is fast enough to generate a new reference trajectory in every guidance cycle. With different cases of the aerodynamic coefficient bias, numerical simulation for the generic hypersonic vehicle model and scramjet engine is done. The results show the accuracy and the effectiveness of the on-board trajectory planning algorithm.

关键词： trajectory planning ascent direct optimisation non-linear programming problem

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