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ON GAP FUNCTIONS FOR QUASI-EQUILIBRIUM PROBLEMS VIA DUALITY
(Springer Nature, 2024-03-06) Lkhamsuren Altangerel
We extend gap functions to quasi-equilibrium problems by using the duality results. In particular, we obtain new results for quasi-equilibrium problems known earlier for equilibrium problems and mixed quasi-variational inequalities. Bibliography: 12 titles.
Gap functions for quasi-variational inequalities via duality
(Springer Nature, 2018-01-10) Altangerel, L.
This paper deals with an application of duality theory in optimization to the construction of gap functions for quasi-variational inequalities. The same approach was investigated for variational inequalities and equilibrium problems in (Pac. J.
Optim. 2(3): 667-678, 2006; Asia-Pac. J. Oper. Res. 24(3): 353-371, 2007), and the study shows that we can obtain some previous results for variational inequalities as special cases. Moreover, some applications dealing with the generalized Nash equilibrium problems and mixed variational inequalities are presented.
Dividends and Compound Poisson-processes: A new Stochastic Stock Price Model
(World Scientific, 2022-05-30) Battulga Gankhuu, Jacob Kleinow, Altangerel Lkhamsuren, Andreas Horsch
This study introduces a stochastic multi-period dividend discount model (DDM) that includes (i) a compound nonhomogenous Poisson process for dividend growth and (ii) the probability of firm default. We obtain maximum likelihood (ML) estimators and confidence interval formulas of our model parameters. We apply the model to a set of firms from the S&P 500 index using historical dividend and price data over a 42-year period. Interestingly, stock price estimations calculated with the model are close to the observable prices. Overall, we prove that the model can be a useful tool for stock pricing.
An Exact Penalty Approach and Conjugate Duality for Generalized Nash Equilibrium Problems with Coupling and Shared Constraints
(Иркутского государственного университета, 2020-09-11) Altangerel, L. & Battur, G.
Generalized Nash Equilibrium Problems (GNEP) have been attracted by many researchers in the field 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 field. 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.
‟Assessment of Soil Erosion, Contamination, and Rehabilitation Potential in Mongolian Mining Regions: A Case Study in the Erdenet Copper and Molybdenum, and Baganuur Coal Mining Areas”
(Von der Fakultät für Georessourcen und Materialtechnik der Rheinisch-Westfälischen Technischen Hochschule Aachen, 2024-07-04) Enkhjargal Sodnomdarjaa, M.; Univ.-Prof. Dr. rer. nat. Frank Lehmkuhl; Prof. Dr. rer. nat. Daniel Karthe
Mining plays a vital role in Mongolia’s economy, contributing significantly to export revenue. However, this economic benefit often comes at the cost of environmental degradation, particularly in regions surrounding major mining sites like the Baganuur lignite mine and the Erdenet copper-molybdenum mine. This study examines the long-term impacts of mining on soil erosion and contamination in Mongolia’s semi-arid steppe zones, aiming to provide insights into the extent of degradation and propose strategies for mitigation and rehabilitation. The study quantifies soil erosion rates in mining regions utilizing the Revised Universal Soil Loss Equation (RUSLE) model, remote sensing data, and ground truth observations spanning nearly three decades (1989-2018). Results show a clear correlation between rainfall erosivity and soil erosion, particularly noting peak erosion in July 2018 in both study areas, reaching 7.88 t ha-1month-1 in the Erdenet area and 9.46 t ha-1month-1 in the Baganuur area. Additionally, the spatial distribution of erosion underscores localized impacts near mining sites and adjacent industrial zones. In addition, erosion due to mining activities has led to soil contamination with Heavy Metals and Metalloids (HMM), posing ecological and health risks. Various indices, such as the Potential Ecological Risk Index (RI), Nemerow Integrated Pollution Index (PIN), and Geoaccumulation Index (Igeo), are used to assess soil contamination levels. Findings reveal elevated concentrations of elements such as Zn and As in the Baganuur mining area, and of Cu, Cr, and Zn in the Erdenet mining area. These concentrations exceed the Maximum Permissible Level (MPL) of Mongolian Soil quality standard (MNS 5850:2019), particularly in proximity to mining and industrial areas. This underscores the urgent need for soil rehabilitation initiatives to mitigate environmental and health hazards. Beyond soil degradation, mining activities have broader environmental and socioeconomic consequences. The study evaluates these impacts, emphasizing the importance of science-based rehabilitation plans and robust implementation of environmental regulations aligned with the United Nations Sustainable Development Goals (UN SDGs). Continuous environmental assessments and rehabilitation initiatives are supported to ensure the long-term sustainability of Mongolia’s mining sector, safeguarding both natural ecosystems and local communities. Based on the study findings, several recommendations emerge for mitigating soil degradation and promoting sustainable mining practices in Mongolia. These include:- Implementation of erosion control measures, such as vegetative cover and terracing, to reduce soil erosion rates in mining regions.
- Adoption of soil remediation techniques, including phytoremediation and chemical stabilization, to address soil contamination and restore ecosystem health.
- Strengthening of environmental regulations and enforcement mechanisms to ensure compliance with national standards and promote responsible mining practices.
- Integration of environmental considerations into mine planning and operation processes, emphasizing the importance of continuous environmental impact assessments and monitoring. By comprehensively understanding the drivers and consequences of soil erosion and contamination, stakeholders such as mining companies, government agencies, local communities, and environmental organizations can collaboratively devise and implement effective mitigation and rehabilitation strategies. This concerted effort aims to ensure the long-term sustainability of Mongolia’s mining sector and the well-being of its inhabitants and wildlife, all while promoting sustainable development.