gradient methods of optimization

gradient methods of optimization
Макаров: градиентные методы оптимизации

Универсальный англо-русский словарь. . 2011.

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  • Optimization (mathematics) — In mathematics, the term optimization, or mathematical programming, refers to the study of problems in which one seeks to minimize or maximize a real function by systematically choosing the values of real or integer variables from within an… …   Wikipedia

  • Gradient descent — For the analytical method called steepest descent see Method of steepest descent. Gradient descent is an optimization algorithm. To find a local minimum of a function using gradient descent, one takes steps proportional to the negative of the… …   Wikipedia

  • Mathematical optimization — For other uses, see Optimization (disambiguation). The maximum of a paraboloid (red dot) In mathematics, computational science, or management science, mathematical optimization (alternatively, optimization or mathematical programming) refers to… …   Wikipedia

  • Multidisciplinary design optimization — Multi disciplinary design optimization (MDO) is a field of engineering that uses optimization methods to solve design problems incorporating a number of disciplines. As defined by Prof. Carlo Poloni, MDO is the art of finding the best compromise …   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

  • Nonlinear conjugate gradient method — In numerical optimization, the nonlinear conjugate gradient method generalizes the conjugate gradient method to nonlinear optimization. For a quadratic function : The minimum of f is obtained when the gradient is 0: . Whereas linear conjugate… …   Wikipedia

  • Conjugate gradient method — A comparison of the convergence of gradient descent with optimal step size (in green) and conjugate vector (in red) for minimizing a quadratic function associated with a given linear system. Conjugate gradient, assuming exact arithmetic,… …   Wikipedia

  • Stochastic optimization — (SO) methods are optimization algorithms which incorporate probabilistic (random) elements, either in the problem data (the objective function, the constraints, etc.), or in the algorithm itself (through random parameter values, random choices,… …   Wikipedia

  • Derivation of the conjugate gradient method — In numerical linear algebra, the conjugate gradient method is an iterative method for numerically solving the linear system where is symmetric positive definite. The conjugate gradient method can be derived from several different perspectives,… …   Wikipedia

  • Shape optimization — is part of the field of optimal control theory. The typical problem is to find the shape which is optimal in that it minimizes a certain cost functional while satisfying given constraints. In many cases, the functional being solved depends on the …   Wikipedia

  • Convex optimization — Convex minimization, a subfield of optimization, studies the problem of minimizing convex functions over convex sets. Given a real vector space X together with a convex, real valued function defined on a convex subset of X, the problem is to find …   Wikipedia


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