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method of multipliers

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  • Lagrange multipliers — In mathematical optimization problems, the method of Lagrange multipliers, named after Joseph Louis Lagrange, is a method for finding the extrema of a function of several variables subject to one or more constraints; it is the basic tool in… …   Wikipedia

  • Lagrange multipliers on Banach spaces — In the field of calculus of variations in mathematics, the method of Lagrange multipliers on Banach spaces can be used to solve certain infinite dimensional constrained optimization problems. The method is a generalization of the classical method …   Wikipedia

  • Gauss pseudospectral method — The Gauss Pseudospectral Method (abbreviated GPM ) is a direct transcription method for discretizing a continuous optimal control problem into a nonlinear program (NLP). The Gauss pseudospectral method differs from several other pseudospectral… …   Wikipedia

  • Newton's method in optimization — A comparison of gradient descent (green) and Newton s method (red) for minimizing a function (with small step sizes). Newton s method uses curvature information to take a more direct route. In mathematics, Newton s method is an iterative method… …   Wikipedia

  • Constrained optimization and Lagrange multipliers — This tutorial presents an introduction to optimization problems that involve finding a maximum or a minimum value of an objective function f(x 1,x 2,ldots, x n) subject to a constraint of the form g(x 1,x 2,ldots, x n)=k.Maximum and… …   Wikipedia

  • optimization — /op teuh meuh zay sheuhn/ 1. the fact of optimizing; making the best of anything. 2. the condition of being optimized. 3. Math. a mathematical technique for finding a maximum or minimum value of a function of several variables subject to a set of …   Universalium

  • Constraint optimization — In constraint satisfaction, constrained optimization (also called constraint optimization) seeks for a solution maximizing or minimizing a cost function. Contents 1 Definition 2 Solution methods 2.1 Branch and bound …   Wikipedia

  • Claude Lemaréchal — is a French applied mathematician. In mathematical optimization, Claude Lemaréchal is known for his work in numerical methods for nonlinear optimization, especially for problems with nondifferentiable kinks. Lemaréchal and Phil. Wolfe pioneered… …   Wikipedia

  • Lagrange multiplier — Figure 1: Find x and y to maximize f(x,y) subject to a constraint (shown in red) g(x,y) = c …   Wikipedia

  • Constraint algorithm — In mechanics, a constraint algorithm is a method for satisfying constraints for bodies that obey Newton s equations of motion. There are three basic approaches to satisfying such constraints: choosing novel unconstrained coordinates ( internal… …   Wikipedia

  • Multiplier (economics) — In economics, a multiplier is a factor of proportionality that measures how much an endogenous variable changes in response to a change in some exogenous variable. For example, suppose a one unit change in some variable x causes another variable… …   Wikipedia

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