Results 1 to 10 of about 603,865 (279)
Hyperbolic Polynomials and Convex Analysis [PDF]
Canadian Journal of Mathematics, 2001 AbstractA homogeneous real polynomialpishyperbolicwith respect to a given vector d if the univariate polynomial t ⟼ p(x − td) has all real roots for all vectorsx. Motivated by partial differential equations, Gårding proved in 1951 that the largest such root is a convex function ofx, and showed various ways of constructing new hyperbolic polynomials. We
Heinz H. Bauschke +3 more
openalex +4 more sources
Convex analysis on polyhedral spaces [PDF]
Mathematische Zeitschrift, 2022 AbstractWe introduce notions of concavity for functions on balanced polyhedral spaces, and we show that concave functions on such spaces satisfy several strong continuity properties.
Botero, Ana Maria +2 more
openaire +4 more sources
Near-Convex Archetypal Analysis [PDF]
IEEE Signal Processing Letters, 2020 Nonnegative matrix factorization (NMF) is a widely used linear dimensionality reduction technique for nonnegative data. NMF requires that each data point is approximated by a convex combination of basis elements. Archetypal analysis (AA), also referred to as convex NMF, is a well-known NMF variant imposing that the basis elements are themselves convex ...
Pierre De Handschutter +3 more
openaire +3 more sources
Mathematical Programming, 2014 International ...
Combettes, Patrick Louis +2 more
openaire +4 more sources
Extreme-value statistics from Lagrangian convex hull analysis for homogeneous turbulent Boussinesq convection and MHD convection [PDF]
, 2017 We investigate the utility of the convex hull of many Lagrangian tracers to analyze transport properties of turbulent flows with different anisotropy. In direct numerical simulations of statistically homogeneous and stationary Navier-Stokes turbulence ...
Busse, A. +4 more
core +5 more sources
Convexity in Real Analysis [PDF]
Real Analysis Exchange, 2011 We treat the classical notion of convexity in the context of hard real analysis. Definitions of the concept are given in terms of defining functions and quadratic forms, and characterizations are provided of different concrete notions of convexity. This analytic notion of convexity is related to more classical geometric ideas.
openaire +4 more sources
Convex analysis and thermodynamics [PDF]
Kinetic & Related Models, 2013 Convex analysis is very useful to prove that a material model fulfills the second law of thermodynamics. Dissipation must remains non-negative and an elegant way to ensure this property is to construct an appropriate pseudo-potential of dissipation.
Point, Nelly, Erlicher, Silvano
openaire +3 more sources
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
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