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Nondominated equilibrium solutions of a multiobjective two-person nonzero-sum game in extensive form and corresponding mathematical programming problem

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JOURNAL OF GLOBAL OPTIMIZATION 2008年第2期42卷 201-220页

作者： Nishizaki, Ichiro Notsu, Takuma Hiroshima Univ Grad Sch Engn Higashihiroshima 7398527 Japan

In most of studies on multiobjective noncooperative games, games are represented in normal form and a solution concept of Pareto equilibrium solutions which is an extension of Nash equilibrium solutions has been focused on. However, for analyzing economic situations and modeling real world applications, we often see cases where the extensive form representation of games is more appropriate than the normal form representation. In this paper, in a multiobjective two-person nonzero-sum game in extensive form, we employ the sequence form of strategy representation to define a nondominated equilibrium solution which is an extension of a Pareto equilibrium solution, and provide a necessary and sufficient condition that a pair of realization plans, which are strategies of players in sequence form, is a nondominated equilibrium solution. Using the necessary and sufficient condition, we formulate a mathematical programming problem yielding nondominated equilibrium solutions. Finally, giving a numerical example, we demonstrate that nondominated equilibrium solutions can be obtained by solving the formulated mathematical programming problem.

关键词： nondominated equilibrium solution multiobjective two-person nonzero-sum game in extensive form mathematical programming problem

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The mathematical programming problem of Total Variation Image Denoising Model

The Mathematical Programming Problem of Total Variation Imag...

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6th International Conference on Wireless Communications, Networking and Mobile Computing (WICOM)

作者： Wan Bao-cheng Wang Tian-e Zhou Tian-tian Jilin Agr Univ Inst Informat Technol Changchun 110118 Peoples R China

ISBN: (纸本)9781424437092

Image denoising is an image processing problem which has a wide use. Total Variation image denoising model is one of the best model at the present time. According to its features, this paper proposes three mathematical programming models which results have the global optimum. The introduction of such model lays the foundation of the further study of mathematical programming models which are relevent to image denosining.

关键词： image denoising mathematical programming mathematical programming problem total variation image denoising model

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On the Second Order Sufficient Optimality Conditions for a problem of mathematical programming

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mathematical NOTES 2024年第1-2期115卷 148-163页

作者： Arutyunov, A. V. Zhukovskiy, S. E. Russian Acad Sci V A Trapeznikov Inst Control Sci Moscow 117997 Russia

We consider the constrained optimization problem for a smooth function defined on a Banach space with smooth constraints of equality and inequality type. We show that for this problem, under the known sufficient secon... 详细信息

关键词： mathematical programming problem Lagrange function sufficient second-order optimality conditions

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Cluster Optimization for Exponential, Right-Triangular, and Uniformly Distributed Data

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IEEE ACCESS 2025年 13卷 36273-36284页

作者： Bulivou, Gabiriele Reddy, Karuna G. Khan, M. G. M. Univ South Pacific Sch Informat Technol Engn Math & Phys Suva Fiji

Cluster analysis aims to categorize data objects into cohesive groups based on their intrinsic characteristics, often modeled by probability distributions. This paper presents a novel mathematical programming-Dynamic programming (MP-DP) clustering method developed by the authors, applied to datasets characterized by exponential, right-triangular, and uniform distributions. The MP-DP technique optimizes cluster partitions by leveraging the probability distributions inherent in the data. We conducted a comparative evaluation to assess the performance of MP-DP against four established clustering methodologies: K-Means, Fuzzy C-Means, expectation-maximization, and Genie++ hierarchical clustering. Results from extensive simulations and real-world datasets consistently demonstrate the superior efficacy of MP-DP in achieving optimal clustering outcomes. Specifically, MP-DP excels in handling diverse data distributions and effectively mitigating the effects of noise and uncertainty, thereby enhancing clustering accuracy and reliability. This study highlights the significant advancement offered by MP-DP in clustering research. It underscores the method's potential for applications across various domains, such as healthcare, environmental monitoring, and manufacturing, where robust and efficient data clustering is essential for insightful data analysis and decision-making.

关键词： Clustering algorithms Probability distribution Dynamic programming programming Noise Clustering methods Partitioning algorithms Heuristic algorithms Distributed databases Uncertainty Cluster analysis dynamic programming technique mathematical programming problem optimum cluster partitions probability distribution function

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mathematical programming problems with quasi-convex objective functions

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mathematical programming 1972年第1期3卷 296-301页

作者： Ferland, Jacques A. Université de Montreal Montreal Canada

关键词： Objective Function mathematical Method programming problem mathematical programming mathematical programming problem

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Robust mathematical programming problems Involving Vanishing Constraints via Strongly Invex Functions

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BULLETIN OF THE MALAYSIAN mathematical SCIENCES SOCIETY 2024年第4期47卷 1-38页

作者： Kummari, Krishna Jaichander, Rekha R. Ahmad, Izhar GITAM Sch Sci Dept Math Hyderabad Campus Hyderabad 502329 Telangana India St Francis Coll Women Begumpet Dept Math Hyderabad 500016 Telangana India King Fahd Univ Petr & Minerals Dept Math Dhahran 31261 Saudi Arabia King Fahd Univ Petr & Minerals Ctr Intelligent Secure Syst Dhahran 31261 Saudi Arabia

This manuscript demonstrates robust optimality conditions, Wolfe and Mond-Weir type robust dual models for a robust mathematical programming problem involving vanishing constraints (RMPVC). Further, the theorems of duality are examined based on the concept of generalized higher order invexity and strict invexity that establish relations between the primal and the Wolfe type robust dual problems. In addition, the duality results for a Mond-Weir type robust dual problem based on the concept of generalized higher order pseudoinvex, strict pseudoinvex and quasiinvex functions are also studied. Furthermore, numerical examples are provided to validate robust optimality conditions and duality theorems of Wolfe and Mond-Weir type dual problems.

关键词： Robust optimization mathematical programming problem Vanishing constraints Duality Strong invexity

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Modifications and extensions of the conjugate gradient-restoration algorithm for mathematical programming problems

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Journal of Optimization Theory and Applications 1971年第6期7卷 450-472页

作者： Miele, A. Levy, A.V. Cragg, E.E. Department of Mechanical and Aerospace Engineering and Materials Science Rice University Houston Texas United States

In this paper, the problem of minimizing a function f(x) subject to a constraint φ{symbol}(x)=0 is considered, where f is a scalar, x an n-vector, and φ{symbol} a q-vector, with q s is such that φ{symbol}(xs)=0, an... 详细信息

关键词： Conjugate Gradient Constraint Violation Previous Algorithm Nonlinear Constraint mathematical programming problem

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Duality questions for improper mathematical programming problems

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Algebra and Logic 1984年第6期23卷 416-425页

作者： Eremin, I.I.

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A multicriteria approach for risk assessment of Covid-19 in urban district lockdown

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SAFETY SCIENCE 2020年 130卷 104862-104862页

作者： Sangiorgio, Valentino Parisi, Fabio Polytech Bari Dept Civil Environm Land Bldg Engn & Chem DICATEC Bari Italy Polytech Bari Dept Elect & Informat Engn DEI Bari Italy

At the beginning of 2020, the spread of a new strand of Coronavirus named SARS-CoV-2 (COVID-19) raised the interest of the scientific community about the risk assessment related to the viral infection. The contagion became pandemic in few months forcing many Countries to declare lockdown status. In this context of quarantine, all commercial and productive activities are suspended, and many Countries are experiencing a serious crisis. To this aim, the understanding of risk of contagion in every urban district is fundamental for governments and administrations to establish reopening strategies. This paper proposes the calibration of an index able to predict the risk of contagion in urban districts in order to support the administrations in identifying the best strategies to reduce or restart the local activities during lockdown conditions. The objective regards the achievement of a useful tool to predict the risk of contagion by considering socio-economic data such as the presence of activities, companies, institutions and number of infections in urban districts. The proposed index is based on a factorial formula, simple and easy to be applied by practitioners, calibrated by using an optimization-based procedure and exploiting data of 257 urban districts of Apulian region (Italy). Moreover, a comparison with a more refined analysis, based on the training of Artificial Neural Networks, is performed in order to take into account the non-linearity of the phenomenon. The investigation quantifies the influence of each considered parameter in the risk of contagion useful to obtain risk analysis and forecast scenarios.

关键词： Risk of Covid-19 contagion Multicriteria analysis Calibration mathematical programming problem Artificial neural networks Apulian Region (Italy)

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A heuristic approach to allocating the continuous resource in discrete-continuous scheduling problems to minimize the makespan

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JOURNAL OF SCHEDULING 2002年第6期5卷 487-499页

作者： Józefowska, J Mika, M Rózycki, R Waligóra, G Weglarz, J Poznan Univ Tech Inst Comp Sci PL-60965 Poznan Poland

A problem of scheduling jobs on parallel, identical machines under an additional continuous resource to minimize the makespan is considered. Jobs are non-preemtable and independent and all are available at the start of the process. The total amount of the continuous resource available at a time is limited and the resource is a renewable one. Each job simultaneously requires for its processing a machine and an amount (unknown in advance) of the continuous resource. The processing rate of a job depends on the amount of the resource allotted to this job at a time. The problem is to find a sequence of jobs on machines and, simultaneously, a continuous resource allocation which minimize the makespan. A heuristic approach to allocating the continuous resource is proposed. A tabu search algorithm to solve the considered problem is presented and the results for the algorithms with exact and heuristic procedures for allocating the continuous resource are compared on the basis of some computational experiments. Copyright (C) 2002 John Wiley Sons, Ltd.

关键词： discrete-continuous scheduling makespan mathematical programming problem heuristic tabu search

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