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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).
The word programming referred to the use of the method to find an optimal program, in the sense of a military schedule for training or logistics. This usage is the same as that in the phrases linear programming and mathematical programming, a synonym for mathematical optimization. [18]
Successive Linear Programming (SLP), also known as Sequential Linear Programming, is an optimization technique for approximately solving nonlinear optimization problems. [1] It is related to, but distinct from, quasi-Newton methods .
Once a system is mathematically modeled, computer-based simulations provide information about its behavior. Parametric simulation methods can be used to improve the performance of a system. In this method, the input of each variable is varied with other parameters remaining constant and the effect on the design objective is observed.
This type of solution concept is called decision set based. [3] It is not compatible with an optimal solution of a linear program but rather parallels the set of all optimal solutions of a linear program (which is more difficult to determine). Efficient points are frequently called efficient solutions. This term is misleading because a single ...
Goal programming is a branch of multiobjective optimization, which in turn is a branch of multi-criteria decision analysis (MCDA). It can be thought of as an extension or generalisation of linear programming to handle multiple, normally conflicting objective measures. Each of these measures is given a goal or target value to be achieved.
Linear–fractional programming (LFP) is a generalization of linear programming (LP). In LP the objective function is a linear function, while the objective function of a linear–fractional program is a ratio of two linear functions. In other words, a linear program is a fractional–linear program in which the denominator is the constant ...
The discovery of linear time algorithms for linear programming and the observation that the same algorithms could in many cases be used to solve geometric optimization problems that were not linear programs goes back at least to Megiddo (1983, 1984), who gave a linear expected time algorithm for both three-variable linear programs and the ...