Many people have the knowledge of linear systems or problems that are common in the field of engineering or generally in sciences. These are usually expressed as vectors. Such systems or problems are also applicable to different forms whereby variables are separated to two subsets that are disjointed with the left-hand side being linear for every separate set. This gives optimization problems that have bilinear objective functions accompanied by one or two constraints, a form known the biliniar problem.
Generally, the bilinear functions are known to have subclasses of quadratic function as well as quadratic programming. This programming usually have several applications such as when dealing with the constrained bi-matrix games, dealing with Markovian assignments, and complementarity problems. At the same time, majority of 0-1 integer programs can be described similarly.
Usually, some similarities may be noted between the linear and the bi-linear systems. For example, both systems have homogeneity in which case the right hand side constants become zero. Additionally, you may add multiples to equations without the need to alter their solutions. At the same time, these problems can further be classified into other two forms that include the complete as well as the incomplete forms. Generally, the complete form usually have distinct solutions other than the number of the variables being the same as the number of the equations.
On the contrary, incomplete forms usually have an indefinite solution that lies in some specified range, and contain more variables compared to the number of equations. In formulating these problems, various forms can be developed. Nonetheless, a more common and practical problem includes the bilinear objective functions that are bound by some constraints that are linear. All expressions taking this form usually have a theoretical result.
These programming problems can also be expressed in form of concave minimization problems, due to their importance in coming up with the concave minimizations. There are two main reasons for this case. First, the bilinear programming may be applied in numerous problems in a real world. Secondly, some techniques often used in solving the bilinear problems have similarities with those techniques often applied in solving the general concave problems in minimization.
The application of these programming problems can be in a number of ways. These include its application in models attempting to represent the circumstances that players in a bimatrix game are faced with. Other areas where it has been previously been used include the decision-making theory, multi-commodity network flows, locating of some newly acquired facilities, multilevel assignment issues as well as in scheduling of orthogonal production.
On the other hand, optimization issues normally connected to bilinear programs remain necessary when undertaking water network operations and even petroleum blending activities around the world. Non-convex-bilinear constraints can be required in the modeling of proportions from different streams that are to be combined in petroleum blending as well as water networking systems.
Also, pooling problems can utilize these forms of equations. Again, such problems in programming have their application in having the solution to various multi-agent coordination as well as planning problems. However, they usually focus on various aspects of Markov process used in decision making.
Generally, the bilinear functions are known to have subclasses of quadratic function as well as quadratic programming. This programming usually have several applications such as when dealing with the constrained bi-matrix games, dealing with Markovian assignments, and complementarity problems. At the same time, majority of 0-1 integer programs can be described similarly.
Usually, some similarities may be noted between the linear and the bi-linear systems. For example, both systems have homogeneity in which case the right hand side constants become zero. Additionally, you may add multiples to equations without the need to alter their solutions. At the same time, these problems can further be classified into other two forms that include the complete as well as the incomplete forms. Generally, the complete form usually have distinct solutions other than the number of the variables being the same as the number of the equations.
On the contrary, incomplete forms usually have an indefinite solution that lies in some specified range, and contain more variables compared to the number of equations. In formulating these problems, various forms can be developed. Nonetheless, a more common and practical problem includes the bilinear objective functions that are bound by some constraints that are linear. All expressions taking this form usually have a theoretical result.
These programming problems can also be expressed in form of concave minimization problems, due to their importance in coming up with the concave minimizations. There are two main reasons for this case. First, the bilinear programming may be applied in numerous problems in a real world. Secondly, some techniques often used in solving the bilinear problems have similarities with those techniques often applied in solving the general concave problems in minimization.
The application of these programming problems can be in a number of ways. These include its application in models attempting to represent the circumstances that players in a bimatrix game are faced with. Other areas where it has been previously been used include the decision-making theory, multi-commodity network flows, locating of some newly acquired facilities, multilevel assignment issues as well as in scheduling of orthogonal production.
On the other hand, optimization issues normally connected to bilinear programs remain necessary when undertaking water network operations and even petroleum blending activities around the world. Non-convex-bilinear constraints can be required in the modeling of proportions from different streams that are to be combined in petroleum blending as well as water networking systems.
Also, pooling problems can utilize these forms of equations. Again, such problems in programming have their application in having the solution to various multi-agent coordination as well as planning problems. However, they usually focus on various aspects of Markov process used in decision making.
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