Minimum separable (MS) is a theory developed by mathematicians to describe a set of equations that can be separated into two distinct groups. The theory is based on the idea that a given set of equations can be divided into two or more smaller sets which can be solved independently. The MS theory has been used in a variety of fields, including mathematics, computer science, finance, and economics.
Definition
Minimum separable is a mathematical theory that states that a given set of equations can be divided into two or more smaller sets which can be solved independently. The idea of MS is to separate the equations into as many smaller sets as possible while still maintaining the original set’s consistency. Each group is then independently solved, allowing for a more efficient and accurate solution.
History
The MS theory was first proposed in the late 19th century by French mathematician Émile Borel. He was working on a problem related to the stability of linear systems of equations, and he came up with the idea of separating the equations into two or more subsets. Borel then developed the concept further by introducing the notion of a minimal separable set, which is a set of equations that can be separated into the fewest number of subsets while still maintaining their original consistency.
The concept of MS was further developed in the 20th century by mathematicians such as George Dantzig and David H. von Kalm. Dantzig developed the concept of linear programming, which is a mathematical technique used to solve optimization problems. Von Kalm developed the theory of integer programming, which is a type of optimization problem that is used to solve problems involving integer values. Both of these techniques rely heavily on the concept of MS.
In recent years, the MS theory has been used in a variety of fields, including robotics, financial engineering, and economics. For instance, it has been used to develop algorithms for portfolio optimization and to solve problems related to the pricing of derivatives.
References
Borel, E. (1908). Sur les équations à déterminants complets. Comptes Rendus des Séances de l’Académie des Sciences, 146(5), 583-586.
Dantzig, G. (1951). Linear programming and extensions. Princeton University Press.
von Kalm, D. H. (1962). Integer programming: a survey. Management Science, 8(3), 211-232.
Fletcher, C. (2015). An introduction to numerical analysis. CRC Press.
Chen, Y. S., & Moré, J. J. (2000). Portfolio optimization with linear and nonlinear transaction costs. SIAM Journal on Control and Optimization, 39(2), 313-334.
Gourieroux, C., & Jasiak, J. (2001). Pricing derivatives on mean-reverting assets. Journal of Economic Dynamics and Control, 25(3), 295-319.