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 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.
With the incomplete forms, however, there are often more variables than the number of equation while the solution to the problem is usually indefinite and falls between a range of values. However, the formulation of such problems assumes various forms. Nonetheless, the often common practical problems are such as objective bilinear function that is followed by one or several other linear constraints. Therefore, theoretical results can be obtained by the expressions which take this form.
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.
These programming problems may be applied in several ways. These applications are such as in models which try to represent circumstances the players of bimatrix games often face. It has also been used previously in decision making theory, locating newly acquired equipment, multi-commodity network flow, multi-level assignment issues and scheduling 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.
The pooling problem as well make use of these forms of problems. Their application also include solving various planning problems and multi-agent coordination. Nonetheless, these generally places focus on numerous features of the Markov process that is commonly used in decision-making process.
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.
With the incomplete forms, however, there are often more variables than the number of equation while the solution to the problem is usually indefinite and falls between a range of values. However, the formulation of such problems assumes various forms. Nonetheless, the often common practical problems are such as objective bilinear function that is followed by one or several other linear constraints. Therefore, theoretical results can be obtained by the expressions which take this form.
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.
These programming problems may be applied in several ways. These applications are such as in models which try to represent circumstances the players of bimatrix games often face. It has also been used previously in decision making theory, locating newly acquired equipment, multi-commodity network flow, multi-level assignment issues and scheduling 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.
The pooling problem as well make use of these forms of problems. Their application also include solving various planning problems and multi-agent coordination. Nonetheless, these generally places focus on numerous features of the Markov process that is commonly used in decision-making process.
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