What is Mathematical optimization?
{{redirect|Optimization}} In many branches of [[science]], including [[mathematics]], '''mathematical optimization''' is a branch that is about finding a right set of answers that gives the best (optimal) solution to a problem, given some limitations, or criteria.<ref>Snyman, J. A. (2005). Practical mathematical optimization (pp. 97-148). Springer Science+ Business Media, Incorporated.</ref><ref>Intriligator, M. D. (2002). Mathematical optimization and economic theory. [[Society for Industrial and Applied Mathematics]].</ref><ref>Luptacik, M. (2010). Mathematical optimization and economic analysis (p. 307). New York, NY, USA:: Springer.</ref> In the simplest case, this means that a [[function (mathematics)|function]] needs to be minimized or maximized. ==Example== For example, consider a baker with a set amount of flour, sugar, yeast, etc. They also are given five hours to prepare. Time and ingredients are the constraints, or criteria. The baker is tasked with providing the largest volume of food to feed a hungry crowd. Maximizing the number of servings is the optimization function. ==Difficulty== Many problems are much harder, though, and solving them [[Mathematical analysis|analytically]] is not feasible: in these cases, [[Numerical analysis|numerical methods]] are often used.<ref>Nocedal, J., & Wright, S. (2006). Numerical optimization. Springer Science & Business Media.</ref><ref>Bonnans, J. F., Gilbert, J. C., Lemaréchal, C., & Sagastizábal, C. A. (2006). Numerical optimization: theoretical and practical aspects. Springer Science & Business Media.</ref> This often is a result of when the decisions that need to be made involve whole numbers. A baker can usually make half of a recipe, but consider a rancher trying to determine how many cattle and sheep to graze. Limitations may include amount of land available or money to purchase the animals. The optimization function is to maximize profit. If they could purchase a fraction of a cow or sheep, then the problem is pretty easy to solve. However, since o