Бидний тухай
Багш ажилтан
Minimax problem has an important role in optimization, global optimization, game theory, and operations research. In [6], optimality conditions have been formulated for the maxmin problem. In a general case, since the maxmin and minimax values are not always equal, therefore, the optimality conditions for the both problems might be di erent. The classical minimax theorem of von Neuman [20] deals with the equality conditions of maxmin and minimax values. In this paper, we derive new optimality conditions for the minimax problem based on Duvobizkii-Milyution theory (Duvobizkii and Milyuton in USSR Comput Math Math Phys 5:1-80, 1965).
Minimax problem has an important role in optimization, global optimization, game theory, and operations research. In [6], optimality conditions have been formulated for the maxmin problem. In a general case, since the maxmin and minimax values are not always equal, therefore, the optimality conditions for the both problems might be di erent. The classical minimax theorem of von Neuman [20] deals with the equality conditions of maxmin and minimax values. In this paper, we derive new optimality conditions for the minimax problem based on Duvobizkii-Milyution theory (Duvobizkii and Milyuton in USSR Comput Math Math Phys 5:1-80, 1965).
Minimax problem has an important role in optimization, global optimization, game theory, and operations research. In [6], optimality conditions have been formulated for the maxmin problem. In a general case, since the maxmin and minimax values are not always equal, therefore, the optimality conditions for the both problems might be di erent. The classical minimax theorem of von Neuman [20] deals with the equality conditions of maxmin and minimax values. In this paper, we derive new optimality conditions for the minimax problem based on Duvobizkii-Milyution theory (Duvobizkii and Milyuton in USSR Comput Math Math Phys 5:1-80, 1965).
Abstract: The paper deals with a Berge equilibrium problem (BEP). Based on the existence results of Berge equilibrium of Nessah, Larbanic and Tazdait [5], we consider BEP with concave objective functions. The existence of BEP has been proven. BEP reduces to nonsmooth optimization problem. Then using a regularized function, we reduce a problem of finding Berge equilibrium to a nonconvex global optimization problem with a differentiable functions. The later allows to apply optimization methods and algorithms to solve the original problem.
Educational quality is perceived differently as it is embedded in its social, cultural, political, and economic circumstances. The current study identified the factors contributing to perceived educational quality in Mongolia and attempted to develop an instrument to measure educational quality using principal component analysis. Using qualitative and quantitative approaches, the analysis yielded 71 items contributing to educational quality in six themes: school environment, school administration, students, parents, curriculum, and teachers. Each theme yielded one to four components as measurable instruments. The study suggests that school conditions should be prioritized to improve educational quality in Mongolia.
Abstract The paper deals with finding a Berge equilibrium by DC optimization method for the global solution. We examine Berge equilibrium [3], [23] in the bimatrix game for mixed strategies. In [5] we proved an existence of Berge equilibrium in the bimatrix game and redusede the bimatrix game to a nonconvex optimization problem. In this paper we show that a new formulated optimization problem can be also reduced to D.C. programming so that one can apply the global optimality conditions [18]. We provide with numerical experiments done for nonzero sum two person game. Keywords Berge equilibrium, Nash equilibrium, d.c. programming, global optimization, global optimality conditions.
Практикын олон бодлого Олон-Лидер-Дагалдагчтай тоглоом, Хоёр түвшний программчлал, Тэнцвэр зааглалттай тэнцвэрийн бодлого руу шилжиж загварчлагддаг. Эдгээр тоглоомд нэг болон хэд хэдэн этгээд эхний шийдвэрийг гаргахад энэхүү шийдвэр дээр үндэслэн бусад дагалдагчид II- түвшинд өөрсдийн хамгийн сайн хариу үйлдлийг гаргаснаар эхний шийдвэр гаргагчид оновчтой стратегиудаа сонгодог дараалалтай. Эдгээр тоглоом нь түвшин бүртээ классик Нэшийн болон ерөнхийлсөн Нэшийн параметртэй тэнцвэрийн бодлого, вариацийн тэнцэтгэл бишүүдэд шилждэг онцлогтой. Бид энэ илтгэлээр дээрх бодлогуудыг холбоо хамаарал, тавилыг танилцуулах зорилготой.
In recent years, the sustainable forest management has been developing in many countries. There are sufficient support and initiatives from policy and legal environment from the government to sustainable utilization of Mongolia’s forest resources. In the past 8 years /2009-2016/ 732 thousand cubic meter wood on average was harvested per year. These included 76-245 thousand cubic meter wood or around 21.6% consumption and 428-702 thousand cubic meter wood or around 78.4% firewood.Based on the calculation, there is a need of approximately 3107901 cubic meter wood for statewide utilization, which will include 1047267 cubic meter wood or 33.7% for consumption and 2060634 cubic meter wood or 66,3% for firewood. To our knowledge, except [3], there are no mathematical models for Mongolian forest resource depletion and operation. Therefore, the main aim of this work is to develop and give decision results based on the use of mathematical modelling. In this study, we propose a dynamical model for interactions between Mongolian forest resource, the possible resource of forest operation and illegal logging. We investigate local stability conditions of the equilibrium points by using some harvesting parameters.
Abstract In this paper, we consider N players nonconvex quadratic generalized Nash equilibrium problems (GNEP) with jointly convex constraints. We show that the problem can be equivalently reduced to the nonconvex unconstrained optimization problem based on a regularized Nikaido-Isoda function and a gap function. The last problem is also nonconvex, so we reduce it to DC (difference of convex functions) optimization problem and then apply local and global methods and algorithms developed by A.S.Strekalovsky [26]. Numerical results are presented. Keywords: Nonconvex games, Nikaido-Isoda function, Gap functions, DC optimization, Local and Global search methods
Educational quality has been discussed extensively. Scholars state that the quality of education is relative to its context embedded in its culture, values, sociopolitical situation as well as economic situation (Mortimore & Stone, 1991; Hanushek, 2002; Scheerens, Luyten, & van Ravens, 2011). It has also been approached from different perspectives such as social justice and capabilities (Tikly & Barrett, 2011), school effectiveness (Cheng, 1999), and an integrated approach of economist and humanist perspectives to define educational quality (Barrett & others, 2006). This study attempts to examine and identify the factors indicating the quality of education in Mongolia using factor analysis. First, we identified major issues of educational quality by collecting and analyzing 66 online media sources. Then, we interviewed 5 specialists in the field to add more clarity in context analysis. Based on the interviews and context analysis, we developed a questionnaire consisting of 123 questions. Participants rated them in terms of their importance (1=least important through 6=most important) to consider the quality of education in Mongolia. The data collection was conducted online, which yielded a valid sample size of 338 participants. We employed exploratory factor analysis to explore important factors of perceived educational quality. The Kaiser-Meyer Olkin measure of sampling adequacy is marvellous (KMO=.904). The total variance explained is .71. Loadings less than .30 was excluded. The preliminary analysis yielded 28 factors such as student individual necessity, student awareness, teacher interaction with students, school interior design, school building outside environment, school administration free from politics and supportive learning atmosphere.
Depletion and deforestation of forest resources are mainly due to industrialization, population, pollution, forest fire, improper commercial logging, and illegal logging in the world. In this paper, we consider two dynamic models. A mathematical Model 1 is proposed considering the forest biomass density urn:x-wiley:08908575:media:nrm12333:nrm12333-math-0001, the density of wood-based industries urn:x-wiley:08908575:media:nrm12333:nrm12333-math-0002 with unknown parameter urn:x-wiley:08908575:media:nrm12333:nrm12333-math-0003. Model 2 is an extension of Model 1 with the density of illegal logging urn:x-wiley:08908575:media:nrm12333:nrm12333-math-0004 with unknown parameter urn:x-wiley:08908575:media:nrm12333:nrm12333-math-0005. It is assumed that the density of forest biomass grows logistically in the absence of wood-based industries and illegal logging. In the proposed models, the controlling parameters urn:x-wiley:08908575:media:nrm12333:nrm12333-math-0006 and urn:x-wiley:08908575:media:nrm12333:nrm12333-math-0007 are crucial parameters for the local stable conditions of the equilibrium points and system control. We also show in this paper that it is possible to control illegal logging by increasing the level of logging by selecting system parameters efficiently and effectively.
In this work, we consider the multi-objective optimization problem based on the circle packing problem, particularly, extending Malfatti's problem (Enkhbat, 2020) with k disks. Malfatti's problem was examined for the rst time from a view point of global optimization theory and algorithm in (Enkhbat, 2016). Also, a game theory approach has been applied to Malfatti's problem in (Enkhbat and Battur, 2021). In this paper, we apply the multi-objective optimization approach to the problem. Using the weighted sum method, we reduce this problem to optimization problem with nonconvex constraints. For solving numerically the weighted sum optimization problem, we apply KKT conditions and nd Pareto stationary points. Also, we estimate upper bounds of the global value of the objective function by Lagrange duality. Numerical results are provided.
In this paper we consider non-cooperative game problem based on the Malfatti's problem. This problem is a special case of generalized Nash equi- librium problems with nonconvex shared constraints. Some numerical results are provided.
In this paper, we consider nonconvex quadratic generalized Nash equilibrium problems. We reformulate a nonconvex unconstrained optimiza- tion problem by using a regularized Nikaido-Isoda function. After that reformulation, we investigate the equivalent DC (difference of two convex functions) problem. Numerical results are presented.
Mongolia has a small open economy that is growing due to its status as one of the major copper exporters in the Asian copper market. We used game theory to analyze the Chinese copper market and determine the competitive strategies used by Mongolian exporters. We show that a variational inequality approach is one option to prove that game theory is applicable in the analysis of the Chinese copper market, as it is spatial and concentrated. To solve the profit maximization problem with a concave objective function for each player and linear strategy set, it can be reduced to variational inequalities. Numerical calculations allow us to predict the responses of certain parameters against external factors or so-called non-economic shocks, such as changes in Chinese import policies, strikes in Chile, etc. In the future, if Mongolia builds a new copper smelter, it will be a competitor within a more concentrated market than that of the current copper concentrate trade. Thus, the importance of developing such a model is increasing.
This paper attempts to study loan interest rate Nash game models in the banking sector under regulatory solvency constraints. By taking solvency constraints as Basel I, Basel II, and Expected Shortfall (ES), we obtain results regarding the existence of loan interest rate equilibrium. A sensitivity analysis for solvency models and some numerical results are presented. Numerical results show that the weighted loan interest rate of the Mongolian banking system is consistent with the base case of the theoretical weighted loan interest rate corresponding to the Nash equilibrium.
Nowadays, consumers have a full of knowledge on products and services, and their daily consumption of healthy and environmentally friendly products has been increasing. Therefore, businesses need to implement green marketing activities, so they need to be aware of environmental issues and consumer needs while maintaining financial sustainabilit y and competitiveness. (Belz & Karstens, 2002). Examples are the rapid growth of organic food products, as consumers are concerned with their health and environmental issues in their day-to-day purchasing decisions. Over 20 years ago, in 1999, the market for organic food products sales was $ 15.2 billion, while sales in 2017 increased to $ 97 billion, indicating that the world's organic food market is growing rapidly. The organic food market is growing by $5 billion a year, and as of 2014, 172 countries have organic food farm land according to the “The World of Organic Agriculture”. Since the market for organic products is a new market for Mongolia, previous surveys in are relatively small. Therefore, this is aimed at conducting a study on behavioral approaches of consumers of organic food products in Ulaanbaatar. We have run statistical and multi-criteria decision making analysis based on given data of consumers. We also apply Harker’s techniques for complete and incomplete evaluation matrices which are defined from consumers decision making. Numerical examples are presented.
Generalized Nash Equilibrium Problems (GNEP) have been attracted by many researchers in the eld of game theory, operational research, engineering, economics as well as telecommunication in recent two decades. One of the most important classes of GNEP is a convex GNEP with jointly convex or shared constraints which has been studied extensively. It is considered to be one of the most challenging classes of problems in the eld. Moreover, there is a gap in the studies on the GNEP with coupling and shared constraints. The aim of this paper is to investigate the relationship between an exact penalty approach and conjugate duality in convex optimization for the GNEP with coupling and shared constraints. In association with necessary optimality conditions, we obtained the parameterized variational inequality problems. This problem has provided an opportunity to solve many other GNEs. Some numerical results are also presented.
Эрчим хүчний зарцуулалт, дэлхийн дулаарал, цаг уурын өөрчлөлт ихтэй энэ үед эрчим хүчний үр ашиг нь эдийн засгийн салбаруудын байгаль орчинд үзүүлж буй нөлөөллийг бууруулах, салбарын өрсөлдөх чадварыг хадгалахад гол үүрэг гүйцэтгэдэг. Нөгөөтэйгөөр, эрчим хүчний хэрэглээний үр ашгийг нэмэгдүүлснээр эрчим хүчний анхдагч бүтээгдэхүүн бүрт зарцуулсан үйлчилгээний үнэ, өртгийг илүү ашигтай зарцуулж болно. Эрчим хүчний үр ашиг нь түүхий түлшний хэрэглээний өсөлтийг сааруулах, эрчим хүчний аюулгүй байдлыг сайжруулах, хүлэмжийн хийн ялгарлыг бууруулахад чухал ач холбогдолтой.
Цахилгаан дамжуулах үндэсний сүлжээ ТӨХК нь монгол орны нутаг дэвсгэр дээр оршиж байгаа цахилгаан, эрчим хүчийг үйлдвэрлэгчдийн үйлдвэрлэсэн цахилгааныг эрчим хүчийг түгээгч байгууллагуудад дамжуулах үйл ажиллаагаа хийдэг үндэсний том хэмжээний төрийн өмчийн байгууллага юм. Энэхүү өгүүлэлд цахилгаан дамжуулах агаарын шугамын ачааллыг оновчтой, үр ашигтайгаар түгээх математик загварыг боловсруулж, уг загварт шаардлагатай коэфициентүүдийг машин сургалтын аргаар олон жилийн дундажийн өгөгдлөөр сургаж ашигласан тухай өгүүлнэ.
The aim of this paper is to investigate the relationship between an exact penalty approach and conjugate duality in convex optimization for the generalized Nash equilibrium problem (for short GNEP) with coupling and shared constraints. In association with necessary optimality conditions, we obtain the parameterized variational inequality problems. Some numerical results are also presented.
The mean pressure in the center of the Siberian anticyclone in January, more than 1030 hPa, in some parts can be up to 1050 hPa. Siberian anticyclone brings very cold (in the surface layers), cloudy and therefore little snow winter in inland areas of Central Asia. During the summer, replaced by Central Asian anticyclone comes depression. Calculate the first three EOFs over the central Asian region for the winter (DJF) season. The first EOF pattern is commonly identified as the Siberian anticyclone oscillation mode. In this study, we apply some applications of principal component analysis (PCA) which is the fundamental technique’s for EOF analysis. Finally, the resulting principal component time series is normalized by the weights used to get the time series of the mean areal amplitudes. Keywords: Siberian anticyclone, PCA, air pressure, air temperature
In this paper we consider the herdsmen problem based on the Malfatti’s problem. This problem is a special case of generalized Nash equilibrium problems for nomadic herdsmen with nonconvex shared constraints. Moreover, we present some numerical results.
Энэ ажлын хүрээнд бид зээлийн хүүгээрээ өрсөлддөг банкны зах зээлд төв банкны шаардах өөрийн хөрөнгийн хүрэлцээний үзүүлэлтийг хангасан байхаар банкууд Нэшийн тэнцвэрд хүргэх зээлийн хүүг хэрхэн тогтоох талаар авч үзсэн. Санамж 4-д буй зээл болон хадгаламжийн хүүний өрсөлдөөний загварыг ашиглан хадгаламжийн хүүнд дээд зааг тавих замаар зээлийн хүү буурна гэсэн маргаанд хариу өгч болно. Өөрийн хөрөнгийн хүрэлцээний зааглалтаар Basel-I, Basel-II-аас шаарддаг өөрийн хөрөнгийн зааглалт мөн Expected Shortfall зааглалтыг авч үзсэн. Загваруудын хувьд тэнцвэрт хүү оршин байхыг баталж, мэдрэмжийн шинжилгээ хийж сонгон авсан гурван банкны хувьд тоон туршилт явуулсан.
This paper deals with an extension of the one-period model in non-life insurance markets (cf. [1]) by using a transition probability matrix depending on some economic factors. We introduce a multi-period model and in each period the solvency constraints will be updated. Moreover, the model has the inactive state including some uninsured population. Similar results on the existence of premium equilibrium and sensitivity analysis for this model are presented and illustrated by numerical results.
This paper deals with an extension of the one-period model in non-life insurance markets (cf. [1]) by using a transition probability matrix depending on some economic factors. We introduce a multi-period model and in each period the solvency constraints will be updated. Moreover, the model has the inactive state including some uninsured population. Similar results on the existence of premium equilibrium and sensitivity analysis for this model are presented and illustrated by numerical results.
Ойөөрөөнөхөнсэргэдэгбайгалийнбаялагболовчойнэкосистемийгхамгаалах,зохистой ашиглах, нөхөн сэргээх байгаль орчин, тогтвортой хөгжлийн шаардлага болон экологийн талаархи засгийн газрын бодлогыг хэрэгжүүлэх үүднээс манай орны байгаль, цаг уурын нөхцөлд тохирсон ойн динамик загвар боловсруулан ойн нөөц баялгийг иж бүрэн зохистой ашиглах, нөхөн сэргээх шаардлагатай байна. Манай орны ойн нөөцийг зохистой ашиглах судалгаа бага хийгдсэн бөгөөд тэдгээр нөлөөллийн зүй тогтлыг илрүүлэх шаардлага зүй ёсоор гарч байна. Тиймээс энэ судалгаа нь ойн нөөцийг доройтуулж байгаа хүчин зүлсийн загвар боловсруулах шинжлэх ухааны үндэслэл болох юм.
Depletion and deforestation of forest resource are mainly due to industrialization, population, pollution, forest fire, improper commercial logging and illegal logging in the world. In this paper we consider mathematical models of forest depletion due to the possible resource of forest operation and illegal logging. In the proposed models, harvesting rate of the forest operation h and harvesting rate of the illegal logging n are crucial parameters for local stable condition of the equilibrium points and the system control. Numerical results are presented.
Ойөөрөөнөхөнсэргэдэгбайгалийнбаялагболовчойнэкосистемийгхамгаалах,зохистой ашиглах, нөхөн сэргээх байгаль орчин, тогтвортой хөгжлийн шаардлага болон экологийн талаархи засгийн газрын бодлогыг хэрэгжүүлэх үүднээс манай орны байгаль, цаг уурын нөхцөлд тохирсон ойн динамик загвар боловсруулан ойн нөөц баялгийг иж бүрэн зохистой ашиглах, нөхөн сэргээх шаардлагатай байна. Манай орны ойн нөөцийг зохистой ашиглах судалгаа бага хийгдсэн бөгөөд тэдгээр нөлөөллийн зүй тогтлыг илрүүлэх шаардлага зүй ёсоор гарч байна. Тиймээс энэ судалгаа нь ойн нөөцийг доройтуулж байгаа хүчин зүлсийн загвар боловсруулах шинжлэх ухааны үндэслэл болох юм.
This paper aims to consider an application of conjugate duality in convex optimization to the generalized Nash equilibrium problemswith shared constraints and nonsmooth cost functions. Sufficient optimality conditions for the problems regarding to players are rewritten as inclusion problems and the maximal monotonicity of setvalued mappings generated by the subdifferentials of functions from data of GNEP is proved. Moreover, some assertions dealing with solutions to GNEP are obtained and applications of splitting algorithms to the oligopolistic market equilibrium models are presented.
