L-convexity L-convex functions and M-convex functionsL-convexityM-convexity L-convex functions and M-convex functionsM-convexitydiscrete convex analysis L-convex functions and M-convex functionsdiscrete convex analysissubmodular functionmatroid L-convex functions and M-convex functionsmatroid...
LetVbe a nonempty finite set andZbe the set of integers. For any functiong :ZV →Z ∪{+∞} define domg = {p ∈ZV : g(p) < +∞}, called theeffective domainofg. A functiong :ZV →Z ∪{+∞} with domg≠∅ is calledL-convexif $$\displaystyle \...
The concepts of L-convexity and M-convexity are introduced by Murota (1996) for functions defined over the integer lattice, and recently extended to polyhedral convex functions by Murota–Shioura (2000). L-convex and M-convex functions are deeply connected with well-solvability in combinatorial op...
We introduce two classes of discrete quasiconvex functions, called quasi M- and L-convex functions, by generalizing the concepts of M- and L-convexity due to Murota (Adv. Math. 124 (1996) 272) and (Math. Programming 83 (1998) 313). We investigate the structure of quasi M- and L-conv...
Submodularity on a tree: Unifying $L^atural$-convex and bisubmodular functions V. Kolmogorov, Submodularity on a tree: Unifying L -convex and bisubmodular functions, in: Proceedings of the 36th International Symposium on Mathematical Foundations of Com- puter Science (MFCS'11), LNCS 6907, ...
I. Jordan. A linearly-convergent stochastic L-BFGS algorithm. In Interna- tional Conference on Artificial Intelligence and Statistics (AISTATS), 2016.P. Moritz, R. Nishihara, and M. I. Jordan. A linearly-convergent stochastic l-bfgs algorithm. In AISTATS, 2016....
-Field of view(convex array): 80 degree -Screen: Smart phone or tablet screen -Supporting system: iOS, Android. -Display mode: B, B/M -Frame rate: 12f/s -Image gray scale: 256 level -Image/video Storage: Store on mobile phones,Tablet PC -Measure: distance, ar...
A library for unconstrained minimization of smooth functions using Newton's method or L-BFGS. - PetterS/spii
We investigate a convex function ψp,q,λ = max{ψp, λψq}, (1 ≤ q < p ≤∞), and its corresponding absolute normalized norm . .ψp,q,λ We determine a dual norm and use it for getting refinements of the classical H¨older inequality. Also, we consider a related concave funct...
For non-convex functions that arise in ML (almost all latent variable models or deep nets), the procedure still works but is only guranteed to converge to a local minimum. In practice, for non-convex optimization, users need to pay more attention to initialization and other algorithm details....