Results 11 to 20 of about 1,126,628 (203)
Sensitivity Analysis for Mirror-Stratifiable Convex Functions [PDF]
, 2018 This paper provides a set of sensitivity analysis and activity identification results for a class of convex functions with a strong geometric structure, that we coined "mirror-stratifiable".
Fadili, Jalal +2 more
core +4 more sources
Quantitative Stability of Linear Infinite Inequality Systems under Block Perturbations with Applications to Convex Systems [PDF]
, 2011 The original motivation for this paper was to provide an efficient quantitative analysis of convex infinite (or semi-infinite) inequality systems whose decision variables run over general infinite-dimensional (resp.
AD Ioffe +22 more
core +5 more sources
Inclusion and Intersection Relations Between Fundamental Classes of Discrete Convex Functions [PDF]
arXiv, 2021 In discrete convex analysis, various convexity concepts are considered for discrete functions such as separable convexity, L-convexity, M-convexity, integral convexity, and multimodularity. These concepts of discrete convex functions are not mutually independent.
arxiv
Shapley-Folkman-type Theorem for Integrally Convex Sets [PDF]
arXiv, 2023 The Shapley-Folkman theorem is a statement about the Minkowski sum of (non-convex) sets, expressing the closeness of the Minkowski sum to convexity in a quantitative manner. This paper establishes similar theorems for integrally convex sets, L-natural-convex sets, and M-natural-convex sets, which are major classes of discrete convex sets in discrete ...
arxiv
Discrete convex analysis [PDF]
Mathematical Programming, 1998 A theory of "discrete convex analysis" is developed for integer-valued functions defined on integer lattice points. The theory parallels the ordinary convex analysis, covering discrete analogues of the fundamental concepts such as conjugacy, subgradients, the Fenchel min-max duality, separation theorems and the Lagrange duality framework for convex ...
openaire +2 more sources
Convexity and logical analysis of data
Theoretical Computer Science, 2000 AbstractA Boolean function is called k-convex if for any pair x,y of its true points at Hamming distance at most k, every point “between” x and y is also true. Given a set of true points and a set of false points, the central question of Logical Analysis of Data is the study of those Boolean functions whose values agree with those of the given points ...
Ekin O., Hammer P.L., Kogan, A.
openaire +5 more sources
Discrete Fenchel Duality for a Pair of Integrally Convex and Separable Convex Functions [PDF]
arXiv, 2021 Discrete Fenchel duality is one of the central issues in discrete convex analysis. The Fenchel-type min-max theorem for a pair of integer-valued M-natural-convex functions generalizes the min-max formulas for polymatroid intersection and valuated matroid intersection.
arxiv
Hyperspace of convex compacta of nonmetrizable compact convex subspaces of locally convex spaces
, 2008 Our main result states that the hyperspace of convex compact subsets of a compact convex subset $X$ in a locally convex space is an absolute retract if and only if $X$ is an absolute retract of weight $\le\omega_1$.
Benyamini +17 more
core +1 more source
Polynomially convex sets whose union has nontrivial hull [PDF]
arXiv, 2021 Several results concerning pairs of polynomially convex sets whose union is not even rationally convex are given. It is shown that there is no restriction on how two spaces can be embedded in some $\C^N$ so as to be polynomially convex but have nonrationally convex union.
arxiv
Sensitivity analysis in convex programming
Computers & Mathematics with Applications, 2009 AbstractThe object of this paper is to perform an analysis of the sensitivity for convex vector programs with inequality constraints by examining the quantitative behavior of a certain set of optima according to changes of right-hand side parameters included in the program.
P. Jiménez Guerra +2 more
openaire +2 more sources