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Multi-objective optimization or Pareto optimization (also known as multi-objective programming, vector optimization, multicriteria optimization, or multiattribute optimization) is an area of multiple-criteria decision making that is concerned with mathematical optimization problems involving more than one objective function to be optimized simultaneously.
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The Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) is a multi-criteria decision analysis method, which was originally developed by Ching-Lai Hwang and Yoon in 1981 [1] with further developments by Yoon in 1987, [2] and Hwang, Lai and Liu in 1993. [3]
In a value function model, the classification rules can be expressed as follows: Alternative i is assigned to group c r if and only if + < < where V is a value function (non-decreasing with respect to the criteria) and t 1 > t 2 > ... > t k−1 are thresholds defining the category limits.
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]
In this example a company should prefer product B's risk and payoffs under realistic risk preference coefficients. Multiple-criteria decision-making (MCDM) or multiple-criteria decision analysis (MCDA) is a sub-discipline of operations research that explicitly evaluates multiple conflicting criteria in decision making (both in daily life and in settings such as business, government and medicine).
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The red curve shows the function f, and the blue lines are the secants. For this particular case, the secant method will not converge to the visible root. In numerical analysis, the secant method is a root-finding algorithm that uses a succession of roots of secant lines to better approximate a root of a function f.