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Linear programming is one of the modest techniques that are applied in optimization. It employs various simple assumptions when solving convoluted problems in optimization. It does this by using linear functions to depict intricate relationships and finding optimum points. While the relationship might be complicated, the use of linear relationships can certainly simplify it. Linear programming has a full range of applications in the real world. For example, if you are driving home on traffic and trying to find the shortest route, then you are using linear programming.
This is an optimization tool with a defined quadratic objective function. It is considered the simplest type of non-linear programming. The objective function is quadratic programming usually has either a second-order polynomial term or a bilinear. Also, its constraints are always linear. Meaning, they can be equalities or inequalities. This type of optimization technique has a myriad of applications. QP is often viewed as a discipline in itself. More importantly, several nonlinear programming algorithms are based on quadratic programming.
In some cases, researchers using linear programming regard certain variable values as fractional instead of integers. This is often done for convenience especially when the variable values are large. However, this is not recommended in most cases. If this happens, you should try to compute a numeric solution with variables that take integer values. Integer programming is the method used to solve programs that has this kind of problem.
This is a technique used to analyze optimization problems with uncertainty. The algorithms take advantage of the aspect that the probability distribution used to govern the data can be estimated or is already known. The objective of stochastic programming is to find a policy that is feasible for all possible data instances and maximize the expectation of the decision and random variables.