A number of individuals are familiar with linear systems or linear problems commonly used in engineering and generally in the field of sciences. These are commonly presented as vectors. Such problems or systems can be extended to other forms in which variables are partitioned to two disjointed subsets, in which case the left-hand-side is linear on each separate set. This gives rise to optimization problems having bilinear objectives together with one or more constraints called the biliniar problem.
Generally, bilinear problems are composed of quadratic function subclasses or even sub-classes of quadratic programming. Such programming can be applied in various instance such as when handling constrained bimatrix games, the handling of Markovian problems of assignment as well as in dealing with complementarity problems. In addition, many 0-1 integer programs can be expressed in the form described earlier.
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.
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 problems are composed of quadratic function subclasses or even sub-classes of quadratic programming. Such programming can be applied in various instance such as when handling constrained bimatrix games, the handling of Markovian problems of assignment as well as in dealing with complementarity problems. In addition, many 0-1 integer programs can be expressed in the form described earlier.
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.
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.
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