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, 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.
Such programming problems can also be presented using concave minimization problems. This is since they are important when developing concave minimizations. This can be explained by two key reasons. First, bilinear programming is applicable in many areas in the reality. Secondly, some of the methods used in solving bilinear programs can be compared to the techniques used in getting solutions to general minimizations involving concave problems.
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.
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.
Such programming problems can also be presented using concave minimization problems. This is since they are important when developing concave minimizations. This can be explained by two key reasons. First, bilinear programming is applicable in many areas in the reality. Secondly, some of the methods used in solving bilinear programs can be compared to the techniques used in getting solutions to general minimizations involving concave problems.
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.
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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