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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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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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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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Coordination of wind generation and demand response to minimise operation cost in day-ahead electricity markets using bi-level optimisation framework

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IET GENERATION TRANSMISSION & DISTRIBUTION 2018年第16期12卷 3793-3802页

作者： Mohammad, Nur Mishra, Yateendra Queensland Univ Technol Sch Elect Engn & Comp Sci George St Brisbane Qld 4000 Australia

Demand response (DR) can play an important role when dealing with the increasing variability of renewables in power system. This study proposes a bi-level market model for wind-integrated electricity market, where the DR requirement is paired with the wind profile to deal with wind variability. At the upper level, an electricity market operator aims to minimise the day-ahead operation cost considering plausible wind generation scenarios. At the lower level, the DR exchange operator aims to maximise social welfare by trading aggregated DR among several aggregators. The solution at this level determines the optimal DR amount and price setting for each aggregator. The DR from the flexible loads is modelled from the end-users' perspective considering their willingness parameter. The market model is formulated as a bi-level optimisation problem using Lagrangian relaxation with Karush-Kuhn-Tucker optimality conditions. The effectiveness of the proposed scheme is demonstrated on sample 4-bus and IEEE 24-bus systems. Different scenarios such as high, medium and low levels of wind and DR are investigated. The high-wind low-DR scenario leads to minimum operation cost and is least inconvenient for end users as it sets the DR at a minimum level while keeping the higher levels of wind generation.

关键词： power generation economics power generation scheduling wind power plants power markets demand side management mathematical programming minimisation associated Karush-Kuhn-Tucker optimality conditions Lagrangian relaxation complementarity constraints mathematical programming problem monetary benefit maximisation DR-capable loads social welfare maximisation DR exchange operator electricity market operator plausible wind generation scenarios wind variability wind profile DR requirement wind-integrated electricity market bilevel market model power system bilevel optimisation framework day-ahead electricity markets day-ahead operation cost minimisation demand response wind generation

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Optimal wind energy bidding strategies in real-time electricity market with multi-energy sources

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IET RENEWABLE POWER GENERATION 2019年第13期13卷 2383-2390页

作者： Zhang, Zijing Chen, Zhi Washington State Univ Sch Engn & Comp Sci Vancouver WA 98686 USA

This study investigates optimal wind power generator bidding strategies in the real-time electricity market. The goal is to maximise its operating profit by determining the optimal amount of wind power to bid in the real-time market. A bi-level stochastic optimisation model is proposed in which the upper-level problem is minimising the negative profit of wind power producers, while the low-level problem clears the real-time market. The uncertainties in the wind power production, thermal power, hydro power, demand, and energy storage are considered in the stochastic model. This study utilises a mathematical programming problem with equilibrium constraints (MPEC) and Karush-Kuhn-Tucker (KKT) conditions to transform the bi-level problem into an equivalent single-level mixed-integer linear problem (MILP). Case studies obtained with the IEEE RTS-24 Bus system demonstrate the effectiveness of the proposed model and the effect of scenarios on the wind power producer's profit.

关键词： stochastic processes profitability power markets integer programming wind power plants power generation economics optimisation stochastic programming mathematical programming linear programming case studies wind power producer optimal wind energy bidding strategies real-time electricity market multienergy sources optimal wind power generator bidding strategies operating profit real-time market bi-level stochastic optimisation model upper-level problem negative profit wind power producers low-level problem wind power production thermal power hydro power energy storage stochastic model mathematical programming problem bi-level problem equivalent single-level mixed-integer linear problem

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Shape-Dependent Velocity Based Droplet Routing on MEDA Biochips

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IEEE ACCESS 2022年 10卷 122423-122430页

作者： Shiro, Chiharu Nishikawa, Hiroki Kong, Xiangbo Tomiyama, Hiroyuki Yamashita, Shigeru Roy, Sudip Ritsumeikan Univ Grad Sch Sci & Engn Kusatsu Shiga 5258577 Japan Osaka Univ Grad Sch Informat Sci & Technol Dept Informat Syst Engn Informat Syst Synth Grp Suita Osaka 5650871 Japan Ritsumeikan Univ Coll Sci & Engn Kusatsu Shiga 5258577 Japan Ritsumeikan Univ Coll Informat Sci & Engn Kusatsu Shiga 5258577 Japan Indian Inst Technol IIT Roorkee Dept Comp Sci & Engn Roorkee 247667 Uttaranchal India

Digital microfluidic biochip (DMFB) has attracted attention in the biochemical and medical industries. In particular, a microelectrode dot array (MEDA) biochip, which is composed of a two-dimensional microelectrode array, enables to realize fine-grained manipulation such as dilution, mixing, sensing, and so on in real-time. Unlike existing DMFB biochips, a MEDA architecture allows microelectrodes to control a certain volume of droplet in a fine-grained manner and can vary droplet volume and shape in such a way that it efficiently conducts synthesis and manipulation of droplets. There have been many works in order to improve the efficiency of synthesis of MEDA biochips;however, the synthesis, especially droplet routing, has never considered the shape-dependent velocity of droplets. In this paper, we propose the droplet routing techniques for MEDA biochips with shape-dependent velocity of droplets. The proposed techniques take the advantage of variant velocities of droplets dependent on the shapes and aim to reduce the overall routing time of a droplet from a source to a destination. Simulation results confirm that the proposed techniques can shorten the routing time by 80% compared to the state-of-the-art techniques.

关键词： Digital microfluidics MEDA droplet routing mathematical programming problem

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Transformed Legendre spectral method for solving infinite horizon optimal control problems

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IMA JOURNAL OF mathematical CONTROL AND INFORMATION 2018年第2期35卷 341-356页

作者： Shahini, M. Mehrpouya, M. A. Gonbad Kavous Univ Fac Basic Sci Dept Math & Stat 163 Basirat BlvdShahid Fallahi St Gonbad Kavous Iran Tafresh Univ Dept Math POB 39518-79611 Tafresh Iran

In this paper, an efficient computational method for numerical solution of infinite horizon optimal control problems is presented. In the proposed method, transformed Legendre spectral scheme is utilized to transcribe the problem to a mathematical programming problem which can be solved by the well-developed optimization algorithms. The main advantages of the present method are obtaining good results and high rate of convergence, while the infinite horizon problem is solved on the original time interval of the problem without transforming it to a finite one. Numerical results of three examples are presented and efficiency of the method is reported.

关键词： optimal control infinite horizon problems spectral methods mathematical programming problem

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