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.
A number of similarities exist between the bilinear systems and the linear systems. For instance, these systems both possess some homogeneity with the constants on the right-hand side identically becoming zero. In addition, an individual can always introduce multiples of such equations to the system of equations without changing their solution. These problems can as well be classified further into two forms including the incomplete and the complete forms. The complete forms generally have some unique solution and with the number of equations and variables being the same.
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.
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.
A number of similarities exist between the bilinear systems and the linear systems. For instance, these systems both possess some homogeneity with the constants on the right-hand side identically becoming zero. In addition, an individual can always introduce multiples of such equations to the system of equations without changing their solution. These problems can as well be classified further into two forms including the incomplete and the complete forms. The complete forms generally have some unique solution and with the number of equations and variables being the same.
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.
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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