Search results
Results from the WOW.Com Content Network
Linear programming (LP), also called linear optimization, is a method to achieve the best outcome (such as maximum profit or lowest cost) in a mathematical model whose requirements and objective are represented by linear relationships. Linear programming is a special case of mathematical programming (also known as mathematical optimization).
Some geometric optimization problems may be expressed as LP-type problems in which the number of elements in the LP-type formulation is significantly greater than the number of input data values for the optimization problem. As an example, consider a collection of n points in the plane, each
It is an optimization problem in mathematics that arises from applications in industry. In terms of computational complexity, the problem is an NP-hard problem reducible to the knapsack problem. The problem can be formulated as an integer linear programming problem.
Cutting planes were proposed by Ralph Gomory in the 1950s as a method for solving integer programming and mixed-integer programming problems. However, most experts, including Gomory himself, considered them to be impractical due to numerical instability, as well as ineffective because many rounds of cuts were needed to make progress towards the solution.
Design optimization applies the methods of mathematical optimization to design problem formulations and it is sometimes used interchangeably with the term engineering optimization. When the objective function f is a vector rather than a scalar, the problem becomes a multi-objective optimization one.
For example, it is not possible to build 3.7 cars. The integer variables represent decisions (e.g. whether to include an edge in a graph) and so should only take on the value 0 or 1. These considerations occur frequently in practice and so integer linear programming can be used in many applications areas, some of which are briefly described below.
We use this example to illustrate the proof of the weak duality theorem. Suppose that, in the primal LP, we want to get an upper bound on the objective 3 x 1 + 4 x 2 {\displaystyle 3x_{1}+4x_{2}} . We can use the constraint multiplied by some coefficient, say y 1 {\displaystyle y_{1}} .
Multi-objective linear programming is a subarea of mathematical optimization. A multiple objective linear program (MOLP) is a linear program with more than one objective function. An MOLP is a special case of a vector linear program. Multi-objective linear programming is also a subarea of Multi-objective optimization.