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 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.
There are various similarities that can be noted between linear systems and bi-linear systems. For instance, both systems have some homogeneity where the right side constants identically become zero. In addition, one can always add multiples to the equations without altering their solutions. On the contrary, these problems can be further classified into two forms, that is the complete and the incomplete forms. The complete forms normally have unique solutions apart from the number of variables being equal to the number of 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 may as well be expressed as concave minimization problems. This is because of their importance when coming up with concave minimizations. Two main reasons exist for this. To begin with, the bilinear programming can be applied to numerous problems in the real world. The second is that some of the techniques utilized when solving bilinear programs bear similarities with the techniques applied in solving general concave problems on minimization.
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.
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 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.
There are various similarities that can be noted between linear systems and bi-linear systems. For instance, both systems have some homogeneity where the right side constants identically become zero. In addition, one can always add multiples to the equations without altering their solutions. On the contrary, these problems can be further classified into two forms, that is the complete and the incomplete forms. The complete forms normally have unique solutions apart from the number of variables being equal to the number of 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 may as well be expressed as concave minimization problems. This is because of their importance when coming up with concave minimizations. Two main reasons exist for this. To begin with, the bilinear programming can be applied to numerous problems in the real world. The second is that some of the techniques utilized when solving bilinear programs bear similarities with the techniques applied in solving general concave problems on minimization.
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.
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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