Live briefing
Everything about Closed convex function
Terms in Maths
In mathematics, a function is said to be closed if for each, the sublevel set is a closed set. Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: Closed convex functionA 5-minute orientation
- Skim a recent paper: Novel Constructions for Closed Convex Cones Through Inequalities and Support FunctionsInfluential work since 2022
- Pick up a classic book: Neural Information ProcessingThe most-reprinted book on the subject
- Read the landmark paper: Multifunctions with convex closed graphCited 141 times
- Go sideways: Self-concordant functionA closely related topic
- Go sideways: Schwartz spaceA closely related topic
📖 Definitions
No dictionary entry for this exact phrase.
🗂️ The subject at a glance
🏆 Landmark papers (most cited)
Multifunctions with convex closed graph
What is the Subdifferential of the Closed Convex Hull of a Function?
A Conical Algorithm for Globally Minimizing a Concave Function Over a Closed Convex Set
Well-positioned Closed Convex Sets and Well-positioned Closed Convex Functions
Every closed convex set is the set of minimizers of some 𝐶^{∞}-smooth convex function
Duality for Closed Convex Functions and Evenly Convex Functions
Minimising quadratic functionals over closed convex cones
Upper semicontinuity of closed-convex-valued multifunctions
🆕 Influential since 2022
Novel Constructions for Closed Convex Cones Through Inequalities and Support Functions
q-Meromorphic closed-to-convex functions related with Janowski function
Analysis of a Modified System of Infectious Disease in a Closed and Convex Subset of a Function Space with Numerical Study
On minimization of quadratic functions over closed convex sets in Hilbert spaces
📚 Books worth reading
Neural Information ProcessingTingwen Huang · 2012
Perturbation theory for linear operatorsTosio Katō · 1966
PTAexamScott M. Giles · 2010
Convergence structures and applications to functional analysisR. Beattie, H.-P. Butzmann · 2002
Asymptotic Geometric AnalysisMonika Ludwig · 2013- 📕Undergraduate convexityNiels Lauritzen · 2013
IJESACBT · 2010- 📕Proceedings of the International Congress of Mathematicians Madrid, August 22-30, 2006Marta Sanz-Solé, Javier Soria · 2007
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
🔗 Related topics
- Self-concordant function A self-concordant function is a function satisfying a certain differential inequality, which makes it particularly easy for optimization using Newton's…
- Schwartz space In mathematics, Schwartz space S {\displaystyle {\mathcal {S}}} is the function space of all functions whose derivatives of all orders are rapidly decreasing…
- Normal cone (convex analysis) In convex analysis and optimization, the normal cone to a set at a point is a convex cone consisting of vectors that make a non-acute angle with every…
- Conic optimization Conic optimization is a subfield of convex optimization that studies problems consisting of minimizing a convex function over the intersection of an affine…
- Gårding's inequality In mathematics, Gårding's inequality is a result that gives a lower bound for the bilinear form induced by a real linear elliptic partial differential…
- Envelope theorem In mathematics and economics, the envelope theorem is a major result about the differentiability properties of the value function of a parameterized optimizatio…
- Kuratowski convergence In mathematics, Kuratowski convergence or Painlevé-Kuratowski convergence is a notion of convergence for subsets of a topological space. First introduced…
- Wolfe conditions In the unconstrained minimization problem, the Wolfe conditions (also known as the Armijo-Wolfe conditions in some books) are a set of inequalities for…