Quadratic programming

Quadratic programming

Quadratic programming

09/10/17

“How can we optimize a nonlinear phenomenon using math?”

 

Linear programming is great for optimizing first order models. However, most real world systems are actually nonlinear in nature and thus require something further than linear programming. So how can we devise a method new, more optimal method? Well, let’s think about it. First, let’s boil everything down into matrices. Then, let’s introduce their constraints. The equation should now be in the form f(x) = 0.5*x^T*B*x – x^T*b subject to A1*x = c and A2*x = d, where x is the set of all independent variables, B and b are any quadratic objective function on these variables, and A1/c and A2/d are the inequality and equality constraints. Once we have the system set up, we can enter it into a computational package and achieve our results. This method is known as quadratic programming and is frequently used to solve problems fields ranging from energy analysis to finance

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