Utility maximization problemUtility maximization was first developed by utilitarian philosophers Jeremy Bentham and John Stuart Mill. In microeconomics, the utility maximization problem is the problem consumers face: "How should I spend my money in order to maximize my utility?" It is a type of optimal decision problem. It consists of choosing how much of each available good or service to consume, taking into account a constraint on total spending (income), the prices of the goods and their preferences.
Logistic regressionIn statistics, the logistic model (or logit model) is a statistical model that models the probability of an event taking place by having the log-odds for the event be a linear combination of one or more independent variables. In regression analysis, logistic regression (or logit regression) is estimating the parameters of a logistic model (the coefficients in the linear combination).
UtilityAs a topic of economics, utility is used to model worth or value. Its usage has evolved significantly over time. The term was introduced initially as a measure of pleasure or happiness as part of the theory of utilitarianism by moral philosophers such as Jeremy Bentham and John Stuart Mill. The term has been adapted and reapplied within neoclassical economics, which dominates modern economic theory, as a utility function that represents a consumer's ordinal preferences over a choice set, but is not necessarily comparable across consumers or possessing a cardinal interpretation.
Global optimizationGlobal optimization is a branch of applied mathematics and numerical analysis that attempts to find the global minima or maxima of a function or a set of functions on a given set. It is usually described as a minimization problem because the maximization of the real-valued function is equivalent to the minimization of the function . Given a possibly nonlinear and non-convex continuous function with the global minima and the set of all global minimizers in , the standard minimization problem can be given as that is, finding and a global minimizer in ; where is a (not necessarily convex) compact set defined by inequalities .
Profit maximizationIn economics, profit maximization is the short run or long run process by which a firm may determine the price, input and output levels that will lead to the highest possible total profit (or just profit in short). In neoclassical economics, which is currently the mainstream approach to microeconomics, the firm is assumed to be a "rational agent" (whether operating in a perfectly competitive market or otherwise) which wants to maximize its total profit, which is the difference between its total revenue and its total cost.
Convex setIn geometry, a subset of a Euclidean space, or more generally an affine space over the reals, is convex if, given any two points in the subset, the subset contains the whole line segment that joins them. Equivalently, a convex set or a convex region is a subset that intersects every line into a single line segment (possibly empty). For example, a solid cube is a convex set, but anything that is hollow or has an indent, for example, a crescent shape, is not convex. The boundary of a convex set is always a convex curve.
Aggregate demandIn macroeconomics, aggregate demand (AD) or domestic final demand (DFD) is the total demand for final goods and services in an economy at a given time. It is often called effective demand, though at other times this term is distinguished. This is the demand for the gross domestic product of a country. It specifies the amount of goods and services that will be purchased at all possible price levels. Consumer spending, investment, corporate and government expenditure, and net exports make up the aggregate demand.
Convex hullIn geometry, the convex hull or convex envelope or convex closure of a shape is the smallest convex set that contains it. The convex hull may be defined either as the intersection of all convex sets containing a given subset of a Euclidean space, or equivalently as the set of all convex combinations of points in the subset. For a bounded subset of the plane, the convex hull may be visualized as the shape enclosed by a rubber band stretched around the subset. Convex hulls of open sets are open, and convex hulls of compact sets are compact.
Design matrixIn statistics and in particular in regression analysis, a design matrix, also known as model matrix or regressor matrix and often denoted by X, is a matrix of values of explanatory variables of a set of objects. Each row represents an individual object, with the successive columns corresponding to the variables and their specific values for that object. The design matrix is used in certain statistical models, e.g., the general linear model.
Multi-objective optimizationMulti-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. Multi-objective is a type of vector optimization that has been applied in many fields of science, including engineering, economics and logistics where optimal decisions need to be taken in the presence of trade-offs between two or more conflicting objectives.
