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Mathematical optimization (alternatively spelled optimisation) or mathematical programming is the selection of a best element, with regard to some criteria, from some set of available alternatives. [1][2] It is generally divided into two subfields: discrete optimization and continuous optimization.
In many applications, objective functions, including loss functions as a particular case, are determined by the problem formulation. In other situations, the decision maker’s preference must be elicited and represented by a scalar-valued function (called also utility function) in a form suitable for optimization — the problem that Ragnar Frisch has highlighted in his Nobel Prize lecture. [4]
Reduced cost. In linear programming, reduced cost, or opportunity cost, is the amount by which an objective function coefficient would have to improve (so increase for maximization problem, decrease for minimization problem) before it would be possible for a corresponding variable to assume a positive value in the optimal solution. It is the ...
Linear programming is a special case of mathematical programming (also known as mathematical optimization). More formally, linear programming is a technique for the optimization of a linear objective function, subject to linear equality and linear inequality constraints. Its feasible region is a convex polytope, which is a set defined as the ...
Price optimization utilizes data analysis to predict the behavior of potential buyers to different prices of a product or service. Depending on the type of methodology being implemented, the analysis may leverage survey data (e.g. such as in a conjoint pricing analysis [7]) or raw data (e.g. such as in a behavioral analysis leveraging 'big data' [8] [9]).
Supply-chain optimization addresses the general supply-chain problem of delivering products to customers at the lowest total cost and highest profit, trading off the costs of inventory, transportation, distributing and manufacturing. In addition, optimizing storage and transportation costs by means of product / package size is one of the ...
Process optimization. Process optimization is the discipline of adjusting a process so as to make the best or most effective use of some specified set of parameters without violating some constraint. Common goals are minimizing cost and maximizing throughput and/or efficiency. Process optimization is one of the major quantitative tools in ...
Bayesian optimization of a function (black) with Gaussian processes (purple). Three acquisition functions (blue) are shown at the bottom. [8]Bayesian optimization is typically used on problems of the form (), where is a set of points, , which rely upon less (or equal to) than 20 dimensions (,), and whose membership can easily be evaluated.