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, the bilinear functions are known to have subclasses of quadratic function as well as quadratic programming. This programming usually have several applications such as when dealing with the constrained bi-matrix games, dealing with Markovian assignments, and complementarity problems. At the same time, majority of 0-1 integer programs can be described similarly.
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.
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 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.
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.
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, the bilinear functions are known to have subclasses of quadratic function as well as quadratic programming. This programming usually have several applications such as when dealing with the constrained bi-matrix games, dealing with Markovian assignments, and complementarity problems. At the same time, majority of 0-1 integer programs can be described similarly.
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.
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 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.
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.
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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