We prove the equidistribution of several multistatistics over some classes permutations avoiding a 3-length pattern. deduce equidistribution, on one hand inv and foze″ statistics, other that maj makl these pattern permutations. Here are celebrated Mahonian is statistics defined in terms generalized patterns 2000 pioneering paper Babson Steingrímsson, by Clarke, Steingrímsson Zeng (1997) [5]. Th...

Bilevel optimization has been developed for many machine learning tasks with large-scale and high-dimensional data. This paper considers a constrained bilevel problem, where the lower-level problem is convex equality inequality constraints upper-level non-convex. The overall objective function non-convex non-differentiable. To solve we develop gradient-based approach, called gradient approximat...

Thanks are due to Qiji Zhu and Halina Strojwas for many useful conversations on this material. Abstract. We provide a highly{reened sequential description of the generalized gradients of Clarke and approximate G{subdiierential of a lower semicontinuous extended{real{valued function deened on a Banach space with a {smooth equivalent renorm. In the case of a Frech et diierentiable renorm we give ...

We show that projected-gradient methods for the distributed computation of generalized Nash equilibria in aggregative games are preconditioned forward-backward splitting methods applied to the KKT operator of the game. Specifically, we adopt the preconditioned forward-backward design, recently conceived by Yi and Pavel in the manuscript “A distributed primal-dual algorithm for computation of ge...

Generalized conditional gradient method has regained increasing research interest as an alternative to another popular proximal gradient method for sparse optimization problems. For particular tasks, its low computation cost of linear subproblem evaluation on each iteration leads to superior practical performance. However, the inferior iteration complexity incurs excess number of gradient evalu...

The spatial structure and temporal evolution of a nondiffusive hot spot is examined in a confined, planar enclosure. The situation is modelled by the reactive Euler equations and single-step Arrhenius kinetics with a large (scaled) activation temperature 1/ . The initial state of the medium is taken to be one of uniform pressure but with a prescribed thermal gradient of order across the domain....

Popular modern generalized gradient approximations are biased toward the description of free-atom energies. Restoration of the first-principles gradient expansion for exchange over a wide range of density gradients eliminates this bias. We introduce a revised Perdew-Burke-Ernzerhof generalized gradient approximation that improves equilibrium properties of densely packed solids and their surfaces.