Journal of Institute of Mathematics and Digital Technology 2023-12-31T03:45:00+00:00 D.Uuganbaatar Open Journal Systems <p>published by the Institute of Mathematics and Digital Technology, Mongolian Academy of Sciences.</p> <p><strong>Abstracting and indexing in <a title="Google Scholar" href="" target="_blank" rel="noopener">Google Scholar</a>, <a title="Studia Archaeologica" href="" target="_blank" rel="noopener">Dimensions</a>. and <a title="EBSCO Discovery service" href="" target="_blank" rel="noopener">EBSCO Discovery service</a></strong></p> Malfatti’s constrained optimization problem 2023-12-28T01:26:42+00:00 Iderbayar Shiilegbat Enkhbat Rentsen <p>In 1803 Italian mathematician Malfatti posed the following problem how to pack three non-overlapping circles of maximum total area in a given triangle. Malfatti originally assumed that the solution to this problem are three circles inscribed in a triangle such that each circle tangent to other two and touches two sides of the triangle. Now it is well known that Malfatti’s solution is not optimal. The problem for the first time was treated as a global optimization problem in Enkhbat [9]. In this paper, we consider a new formulation of Malfatti’s problem called Malfatti’s constrained optimization problem. The new problem is formulated as a nonconvex optimization problem with nonlinear constraints. Numerical experiments were conducted on Python for the cases.</p> 2023-12-31T00:00:00+00:00 Copyright (c) 2023 Iderbayar Shiilegbat, Enkhbat Rentsen Comparison of Nash and Berge Equilibrium’s in Bimatrix Game 2023-12-28T01:22:30+00:00 Mengkezula Sagaarinqin Batbileg Sukhee <p>Game theory has numerous applications in applied mathematics, economics, and decision theory. There are several books and articles that deal with Nash and Berge equilibriums. To our knowledge, there are no comparisons or conclusive results related to the optimal decision-making between Nash and Berge equilibriums. We provide numerical experiments for both equilibria.</p> <p><strong>Биматрицан Тоглоом Дахь Нэш, Бержийн Тэнцвэрийн Харьцуулалт</strong></p> <p><strong>Хураангуй:</strong> Тоглоомын онол нь эдийн засаг, шийдвэр гаргалтын онол, бизнес, улс төр, хэрэглээний математик зэрэг салбарт хэрэглээ ихтэй. Бержийн тэнцвэрийн талаар хэд хэдэн судалгаа, зохиолууд байдаг боловч бидний одоогийн судалснаар түүний Бержийн тэнцвэрийн оновчтой шийдийн хувьд Нэшийн тэнцвэртэй харьцуулсан судалгааны ажил байхгүй байна. Бидний ажил нь энэ харьцуулалтыг хийж Берж ба Нэшийн тэнцвэрүүдийн хувьд тоглогчдын хожлын утгын хувьд харьцуулсан дүгнэлт гаргах зорилготой. Тоон туршилт хийж үр дүнг гаргасан.<br /><strong>Түлхүүр үгс</strong>: Бержийн ба Нэшийн тэнцвэр, локал ба глобал оновчтой шийд, глобал оновчтой<br />нөхцөл</p> 2023-12-31T00:00:00+00:00 Copyright (c) 2023 Mengkezula Sagaarinqin, Batbileg Sukhee