31 relations: Absolute value, Claude Lemaréchal, Closed set, Compact space, Convex analysis, Convex function, Convex optimization, Convex set, Derivative, Dot product, Dual space, Empty set, Euclidean space, If and only if, Interval (mathematics), Jean-Jacques Moreau, John Wiley & Sons, Locally convex topological vector space, Mathematics, Maxima and minima, Minkowski addition, One-sided limit, Open set, R. Tyrrell Rockafellar, Real number, Set (mathematics), Singleton (mathematics), Slope, Subgradient method, Unbounded operator, Weak derivative.
In mathematics, the absolute value or modulus of a real number is the non-negative value of without regard to its sign.
Claude Lemaréchal is a French applied mathematician, and former senior researcher (directeur de recherche) at INRIA near Grenoble, France.
In geometry, topology, and related branches of mathematics, a closed set is a set whose complement is an open set.
In mathematics, and more specifically in general topology, compactness is a property that generalizes the notion of a subset of Euclidean space being closed (that is, containing all its limit points) and bounded (that is, having all its points lie within some fixed distance of each other).
Convex analysis is the branch of mathematics devoted to the study of properties of convex functions and convex sets, often with applications in convex minimization, a subdomain of optimization theory.
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.
Convex optimization is a subfield of optimization that studies the problem of minimizing convex functions over convex sets.
In convex geometry, a convex set is a subset of an affine space that is closed under convex combinations.
The derivative of a function of a real variable measures the sensitivity to change of the function value (output value) with respect to a change in its argument (input value).
In mathematics, the dot product or scalar productThe term scalar product is often also used more generally to mean a symmetric bilinear form, for example for a pseudo-Euclidean space.
In mathematics, any vector space V has a corresponding dual vector space (or just dual space for short) consisting of all linear functionals on V, together with the vector space structure of pointwise addition and scalar multiplication by constants.
In mathematics, and more specifically set theory, the empty set or null set is the unique set having no elements; its size or cardinality (count of elements in a set) is zero.
In geometry, Euclidean space encompasses the two-dimensional Euclidean plane, the three-dimensional space of Euclidean geometry, and certain other spaces.
In logic and related fields such as mathematics and philosophy, if and only if (shortened iff) is a biconditional logical connective between statements.
In mathematics, a (real) interval is a set of real numbers with the property that any number that lies between two numbers in the set is also included in the set.
Jean Jacques Moreau (31 July 1923 – 9 January 2014) was a French mathematician and mechanician.
John Wiley & Sons, Inc., also referred to as Wiley, is a global publishing company that specializes in academic publishing.
In functional analysis and related areas of mathematics, locally convex topological vector spaces or locally convex spaces are examples of topological vector spaces (TVS) that generalize normed spaces.
Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") is the study of such topics as quantity, structure, space, and change.
In mathematical analysis, the maxima and minima (the respective plurals of maximum and minimum) of a function, known collectively as extrema (the plural of extremum), are the largest and smallest value of the function, either within a given range (the local or relative extrema) or on the entire domain of a function (the global or absolute extrema).
In geometry, the Minkowski sum (also known as dilation) of two sets of position vectors A and B in Euclidean space is formed by adding each vector in A to each vector in B, i.e., the set Analogously, the Minkowski difference (or geometric difference) is defined as It is important to note that in general A - B\ne A+(-B).
In calculus, a one-sided limit is either of the two limits of a function f(x) of a real variable x as x approaches a specified point either from below or from above.
In topology, an open set is an abstract concept generalizing the idea of an open interval in the real line.
Ralph Tyrrell Rockafellar (born February 10, 1935) is an American mathematician and one of the leading scholars in optimization theory and related fields of analysis and combinatorics.
In mathematics, a real number is a value of a continuous quantity that can represent a distance along a line.
In mathematics, a set is a collection of distinct objects, considered as an object in its own right.
In mathematics, a singleton, also known as a unit set, is a set with exactly one element.
In mathematics, the slope or gradient of a line is a number that describes both the direction and the steepness of the line.
Subgradient methods are iterative methods for solving convex minimization problems.
In mathematics, more specifically functional analysis and operator theory, the notion of unbounded operator provides an abstract framework for dealing with differential operators, unbounded observables in quantum mechanics, and other cases.
In mathematics, a weak derivative is a generalization of the concept of the derivative of a function (strong derivative) for functions not assumed differentiable, but only integrable, i.e., to lie in the L''p'' space \mathrm^1().