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Constraint (mathematics) In mathematics, a constraint is a condition of an optimization problem that the solution must satisfy. There are several types of constraints—primarily equality constraints, inequality constraints, and integer constraints. The set of candidate solutions that satisfy all constraints is called the feasible set.
Constrained optimization. In mathematical optimization, constrained optimization (in some contexts called constraint optimization) is the process of optimizing an objective function with respect to some variables in the presence of constraints on those variables. The objective function is either a cost function or energy function, which is to ...
Budget constraint. In economics, a budget constraint represents all the combinations of goods and services that a consumer may purchase given current prices within their given income. Consumer theory uses the concepts of a budget constraint and a preference map as tools to examine the parameters of consumer choices .
One or more of the particles may each be subject to one or more holonomic constraints; such a constraint is described by an equation of the form f(r, t) = 0. If the number of constraints in the system is C, then each constraint has an equation f 1 (r, t) = 0, f 2 (r, t) = 0,..., f C (r, t) = 0, each of which
Holonomic constraints. In classical mechanics, holonomic constraints are relations between the position variables (and possibly time) [1] that can be expressed in the following form: where are n generalized coordinates that describe the system (in unconstrained configuration space). For example, the motion of a particle constrained to lie on ...
Lagrange multiplier. In mathematical optimization, the method of Lagrange multipliers is a strategy for finding the local maxima and minima of a function subject to equation constraints (i.e., subject to the condition that one or more equations have to be satisfied exactly by the chosen values of the variables). [1]
A Bellman equation, named after Richard E. Bellman, is a necessary condition for optimality associated with the mathematical optimization method known as dynamic programming. [1] It writes the "value" of a decision problem at a certain point in time in terms of the payoff from some initial choices and the "value" of the remaining decision ...
Constrained least squares. In constrained least squares one solves a linear least squares problem with an additional constraint on the solution. [1][2] This means, the unconstrained equation must be fit as closely as possible (in the least squares sense) while ensuring that some other property of is maintained.