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.
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.
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.
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.
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.
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.
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.
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.
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.
About the Author:
Find out how to solve the biliniar problem for optimization purposes when you review the essential facts online. Get all the details by clicking on this link http://igbu.co.
No comments:
Post a Comment