As a matter of fact, some people are actually familiar the linear systems often used in engineering or simply in sciences. In most cases, they are presented as vectors. These kind of systems or problems may be extended to different forms where variables are usually partitioned into two disjointed subsets. In such a case the left side is linear on every separate set. As a result, it gives rise to the optimization problems when having the bilinear goals together with either one or several constraints known as biliniar problem.
Generally, bilinear functions are said to be composed of subclasses of quadratic functions and even quadratic programming. Such programming normally has a number of applications for example when dealing with constrained bi-matrix games, complementarity problems as well as when handling Markovian assignment problems. In addition, most of the 0-1 integer programs are able to be described in a similar way.
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.
Additionally, optimization problems involving bilinear programs may also be necessary in petroleum blending activities and water networks operations all over the world. The non-convex bilinear constraints are also highly needed in modeling the proportions that are to be mixed from the different streams in petroleum blending as well as in water network systems.
A pooling problem also utilizes these form of equations. Such a problem in programming also has its application in getting the solution to a number of multi-agent coordination and planning problems. Nevertheless, these usually focus on the various aspects of the Markov process of decision making.
Generally, bilinear functions are said to be composed of subclasses of quadratic functions and even quadratic programming. Such programming normally has a number of applications for example when dealing with constrained bi-matrix games, complementarity problems as well as when handling Markovian assignment problems. In addition, most of the 0-1 integer programs are able to be described in a similar way.
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.
Additionally, optimization problems involving bilinear programs may also be necessary in petroleum blending activities and water networks operations all over the world. The non-convex bilinear constraints are also highly needed in modeling the proportions that are to be mixed from the different streams in petroleum blending as well as in water network systems.
A pooling problem also utilizes these form of equations. Such a problem in programming also has its application in getting the solution to a number of multi-agent coordination and planning problems. Nevertheless, these usually focus on the various aspects of the Markov process of decision making.
About the Author:
Find out how to solve the biliniar problem for optimization purposes when you review the essential facts online. Get all the details by clicking on this link http://igbu.co.
No comments:
Post a Comment