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Subgradient method

Index Subgradient method

Subgradient methods are iterative methods for solving convex minimization problems. [1]

16 relations: Andrzej Piotr Ruszczyński, Claude Lemaréchal, Convex function, Convex optimization, Convex set, Dimitri Bertsekas, Gradient descent, Interior-point method, Iterative method, Level set, Mathematical proof, Naum Z. Shor, Norm (mathematics), Princeton University Press, Springer Science+Business Media, Subderivative.

Andrzej Piotr Ruszczyński

Andrzej Piotr Ruszczyński (born July 29, 1951) is a Polish-American applied mathematician, noted for his contributions to mathematical optimization, in particular, stochastic programming and risk-averse optimization.

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Claude Lemaréchal

Claude Lemaréchal is a French applied mathematician, and former senior researcher (directeur de recherche) at INRIA near Grenoble, France.

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Convex function

In mathematics, a real-valued function defined on an ''n''-dimensional interval is called convex (or convex downward or concave upward) if the line segment between any two points on the graph of the function lies above or on the graph, in a Euclidean space (or more generally a vector space) of at least two dimensions.

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Convex optimization

Convex optimization is a subfield of optimization that studies the problem of minimizing convex functions over convex sets.

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Convex set

In convex geometry, a convex set is a subset of an affine space that is closed under convex combinations.

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Dimitri Bertsekas

Dimitri Panteli Bertsekas (b. 1942, Athens, Δημήτρης Παντελής Μπερτσεκάς) is an applied mathematician, electrical engineer, and computer scientist, and a professor at the department of Electrical Engineering and Computer Science in School of Engineering at the Massachusetts Institute of Technology (MIT), Cambridge, Massachusetts.

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Gradient descent

Gradient descent is a first-order iterative optimization algorithm for finding the minimum of a function.

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Interior-point method

Interior-point methods (also referred to as barrier methods) are a certain class of algorithms that solve linear and nonlinear convex optimization problems.

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Iterative method

In computational mathematics, an iterative method is a mathematical procedure that uses an initial guess to generate a sequence of improving approximate solutions for a class of problems, in which the n-th approximation is derived from the previous ones.

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Level set

In mathematics, a level set of a real-valued function ''f'' of ''n'' real variables is a set of the form that is, a set where the function takes on a given constant value c. When the number of variables is two, a level set is generically a curve, called a level curve, contour line, or isoline.

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Mathematical proof

In mathematics, a proof is an inferential argument for a mathematical statement.

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Naum Z. Shor

Naum Zuselevich Shor (Наум Зуселевич Шор) (1 January 1937 – 26 February 2006) was a Soviet and Ukrainian Jewish mathematician specializing in optimization.

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Norm (mathematics)

In linear algebra, functional analysis, and related areas of mathematics, a norm is a function that assigns a strictly positive length or size to each vector in a vector space—save for the zero vector, which is assigned a length of zero.

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Princeton University Press

Princeton University Press is an independent publisher with close connections to Princeton University.

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Springer Science+Business Media

Springer Science+Business Media or Springer, part of Springer Nature since 2015, is a global publishing company that publishes books, e-books and peer-reviewed journals in science, humanities, technical and medical (STM) publishing.

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Subderivative

In mathematics, the subderivative, subgradient, and subdifferential generalize the derivative to functions which are not differentiable.

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Redirects here:

Bundle method, Nonsmooth minimization, Subgradient methods.

References

[1] https://en.wikipedia.org/wiki/Subgradient_method

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