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 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.
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.
There are various scenarios in which these programming problems remain applicable. These include the representation of situations such as the ones facing bimatrix game players. Other areas of previous successful use are such as multi-commodity flow networks, multilevel assignment problems, decision-making theory, scheduling orthogonal production as well as locating of a freshly acquired facility.
In addition, optimization problems usually involving bilinear programs are also necessary when conducting petroleum blending activities as well as water networks operations across the globe. Non-convex-bilinear constraints are mostly needed when modeling the proportions to be mixed from different streams within the petroleum blending and 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.
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.
There are various scenarios in which these programming problems remain applicable. These include the representation of situations such as the ones facing bimatrix game players. Other areas of previous successful use are such as multi-commodity flow networks, multilevel assignment problems, decision-making theory, scheduling orthogonal production as well as locating of a freshly acquired facility.
In addition, optimization problems usually involving bilinear programs are also necessary when conducting petroleum blending activities as well as water networks operations across the globe. Non-convex-bilinear constraints are mostly needed when modeling the proportions to be mixed from different streams within the petroleum blending and 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.
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