We study two techniques to obtain new families of classical and general DualFeasible Functions: A conversion from minimal Gomory–Johnson functions; and computer-based search using polyhedral computation and an automatic maximality and extremality test.

In this paper, we consider the Lagrangian dual problem of a class of convex optimization problems. We first discuss the semismoothness of the Lagrangian-dual function φ. This property is then used to investigate the second-order properties of the Moreau-Yosida regularization η of the function φ, e.g., the semismoothness of the gradient g of the regularized function η. We show that φ and g are p...

Proteostasis imbalance is emerging as a major hallmark of cancer, driving tumor aggressiveness. Evidence suggests that the endoplasmic reticulum (ER), a major site for protein folding and quality control, plays a critical role in cancer development. This concept is valid in glioblastoma multiform (GBM), the most lethal primary brain cancer with no effective treatment. We previously demonstrated...

In this paper, we will give the subconvexity bounds for self-dual GL(3) L-functions in the t aspect as well as subconvexity bounds for self-dual GL(3) × GL(2) L-functions in the GL(2) spectral aspect.

In this paper, we investigate the effects of pollution error on the performance of the parallel adaptive finite element technique proposed by Bank and Holst in 2000. In particular, we consider whether the performance of the algorithm as it was originally proposed can be improved through the use of certain dual functions which give indication of global influences on subdomain errors.

The k-Schur functions were first introduced by Lapointe, Lascoux and Morse [18] in the hopes of refining the expansion of Macdonald polynomials into Schur functions. Recently, an alternative definition for k-Schur functions was given by Lam, Lapointe, Morse, and Shimozono [17] as the weighted generating function of starred strong tableaux which correspond with labeled saturated chains in the Br...

Reelin coordinates the movements of neurons during brain development by signaling through the Dab1 adaptor and Src family tyrosine kinases. Experiments with cultured neurons have shown that when Dab1 is phosphorylated on tyrosine, it activates Akt and provides a scaffold for assembling signaling complexes, including the paralogous Crk and CrkL adaptors. The roles of Akt and Dab1 complexes durin...

We investigate novel, dual algorithms for dynamic programming and reinforcement learning, based on maintaining explicit representations of stationary distributions instead of value functions. In particular, we investigate the convergence properties of standard dynamic programming and reinforcement learning algorithms when they are converted to their natural dual form. Here we uncover advantages...

We study the bandwidth allocation problem Maximize U(x), subject to Ax ≤ c;x ≥ 0 where U is a utility function, x is a bandwidth allocation vector, and Ax ≤ c represent the capacity constraints. We consider the class of canonical utility functions, consisting of functions U that are symmetric, non-decreasing, concave, and satisfy U(0) = 0. Natural primal-dual algorithms exist for maximizing suc...