A class Ψ of strictly concave and twice continuously differentiable functions ψ : R → R with particular properties is used for constraint transformation in the framework of a Nonlinear Rescaling (NR) method with “dynamic” scaling parameter updates. We show that the NR method is equivalent to the Interior Quadratic Prox method for the dual problem in a rescaled dual space. The equivalence is use...

We consider an algorithm that successively samples and minimizes stochastic models of the objective function. We show that under weak-convexity and Lipschitz conditions, the algorithm drives the expected norm of the gradient of the Moreau envelope to zero at the rate O(k−1/4). Our result yields the first complexity guarantees for the stochastic proximal point algorithm on weakly convex problems...

The NC-proximal average is a parametrized function used to continuously transform one proper, lsc, prox-bounded function into another. Until now it has been defined for two functions. The purpose of this article is to redefine it so that any finite number of functions may be used. The layout generally follows that of [11], extending those results to the more general case and in some instances g...

We discuss in this paper asymptotics of locally optimal solutions of maximum likelihood and, more generally,M-estimation procedures in cases where the true value of the parameter vector lies on the boundary of the parameter set S. We give a counterexample showing that regularity of S in the sense of Clarke is not sufficient for asymptotic equivalence of √ n-consistent locally optimal M-estimato...

We study the well-posedness of a class of nonlocal-interaction equations on general domains Ω⊂Rd , including nonconvex ones. We show that under mild assumptions on the regularity of domains (uniform prox-regularity), for λ -geodesically convex interaction and external potentials, the nonlocal-interaction equations have unique weak measure solutions. Moreover, we show quantitative estimates on t...

Determining the “active manifold” for a minimization problem is a large step towards solving the problem. Many researchers have studied under what conditions certain algorithms identify active manifolds in a finite number of iterations. In this work we outline a unifying framework encompassing many earlier results on identification via the Subgradient (Gradient) Projection Method, Newton-like M...

We consider minimization of functions that are compositions of prox-regular functions with smooth vector functions. A wide variety of important optimization problems can be formulated in this way. We describe a subproblem constructed from a linearized approximation to the objective and a regularization term, investigating the properties of local solutions of this subproblem and showing that the...

Background—Emerging evidence has suggested a contribution of bone marrow (BM) cells to lymphatic vessel formation; however, the exact phenotype of the cells with lymphatic endothelial progenitor cell function has yet to be identified. Here, we investigate the identity of BM-derived lymphatic endothelial progenitor cells and their role in lymphatic neovascularization. Methods and Results—Culture...

In recent years, nanostructured Au catalysts have attracted a lot of attention as potential candidates for the removal of poisonous carbon monoxide from synthesis gas streams, thus upgrading hydrogen gas to be used as fuel at the anode of lowtemperature fuel cells. The interest in Au nanoparticles has been motivated by the pioneering work of Haruta et al., who demonstrated the extremely high ac...