Results 21 to 30 of about 1,126,628 (203)
Differential analysis of matrix convex functions
, 2006 We analyze matrix convex functions of a fixed order defined on a real interval by differential methods as opposed to the characterization in terms of divided differences given by Kraus.
Akritas +11 more
core +2 more sources
Applications of convex analysis within mathematics [PDF]
Mathematical Programming, 2013 38 pages, minor revision incorporating referees ...
Aragón Artacho, Francisco J. +3 more
openaire +6 more sources
Continuous essential selections and integral functionals
, 2013 Given a strictly positive measure, we characterize inner semicontinuous solid convex-valued mappings for which continuous functions which are selections almost everywhere are selections.
Perkkiö, Ari-Pekka
core +1 more source
Convex analysis and financial equilibrium [PDF]
Mathematical Programming, 2014 Convexity has long had an important role in economic theory, but some recent developments have featured it all the more in problems of equilibrium. Here the tools of convex analysis are applied to a basic model of incomplete financial markets in which assets are traded and money can be lent or borrowed between the present and future.
Jofre, A. +2 more
openaire +3 more sources
A new treatment of convex functions [PDF]
arXiv, 2020 Convex functions have played a major role in the field of Mathematical inequalities. In this paper, we introduce a new concept related to convexity, which proves better estimates when the function is somehow more convex than another. In particular, we define what we called $g-$convexity as a generalization of $\log-$convexity.
arxiv
A geometric approach to second-order differentiability of convex functions [PDF]
arXiv, 2023 We show a new, elementary and geometric proof of the classical Alexandrov theorem about the second order differentiability of convex functions. We also show new proofs of recent results about Lusin approximation of convex functions and convex bodies by $C^{1,1}$ convex functions and convex bodies.
arxiv
Sharp boundary regularity for some degenerate-singular Monge-Ampère Equations on k-convex domain [PDF]
arXiv, 2023 We introduce the concept of k-strictly convexity to describe the accurate convexity of convex domains some directions of which boundary may be flat. Basing this accurate convexity, we construct sub-solutions the Dirichlet problem for some degenerate-singular Monge-Amp\`ere type equations and prove the sharp boundary estimates for convex viscosity ...
arxiv
Variational Methods in Convex Analysis [PDF]
Journal of Global Optimization, 2006 We use variational methods to provide a concise development of a number of basic results in convex and functional analysis. This illuminates the parallels between convex analysis and smooth subdifferential theory.
Borwein, Jonathan M., Zhu, Qiji J.
openaire +2 more sources
Decomposition of an Integrally Convex Set into a Minkowski Sum of Bounded and Conic Integrally Convex Sets [PDF]
arXiv, 2023 Every polyhedron can be decomposed into a Minkowski sum (or vector sum) of a bounded polyhedron and a polyhedral cone. This paper establishes similar statements for some classes of discrete sets in discrete convex analysis, such as integrally convex sets, L-natural-convex sets, and M-natural-convex sets.
arxiv
A convex-analysis perspective on disjunctive cuts [PDF]
Mathematical Programming, 2005 We treat the general problem of cutting planes with tools from convex analysis. We emphasize the case of disjunctive polyhedra and the generation of facets. We conclude with some considerations on the design of efficient cut generators.
Cornuéjols, Gérard +1 more
openaire +5 more sources