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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.
Pattern search (also known as direct search, derivative-free search, or black-box search) is a family of numerical optimization methods that does not require a gradient. As a result, it can be used on functions that are not continuous or differentiable. One such pattern search method is "convergence" (see below), which is based on the theory of ...
Kalai and Smorodinsky differ from Nash on this issue. They claim that the entire set of alternatives must affect the agreement reached. In the above example, suppose the preference relation of player 2 is: C>>B>A (C is much better than B, which is somewhat better than A) while the preference relation of 1 is reversed: A>>B>>C.
If the preference set is convex, then the consumer's set of optimal decisions is a convex set, for example, a unique optimal basket (or even a line segment of optimal baskets). For simplicity, we shall assume that the preferences of a consumer can be described by a utility function that is a continuous function , which implies that the ...
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 other words: a preference relation is quasilinear if there is one commodity, called the numeraire, which shifts the indifference curves outward as consumption of it increases, without changing their slope. In the two dimensional case, the indifference curves are parallel. This is useful because it allows the entire utility function to be ...
Choice modelling attempts to model the decision process of an individual or segment via revealed preferences or stated preferences made in a particular context or contexts. Typically, it attempts to use discrete choices (A over B; B over A, B & C) in order to infer positions of the items (A, B and C) on some relevant latent scale (typically ...
All the responses are recorded and form the person's preference relation. Instead of recording the person's preferences between every pair of options, it would be much more convenient to have a single utility function - a function that maps a real number to each option, such that the utility of option A is larger than that of option B if and ...