We present a new algorithm to compute the Legendre–Fenchel conjugate of convex piecewise linear-quadratic (PLQ) bivariate functions. The algorithm stores a function using a (primal) planar arrangement. It then computes the (dual) arrangement associated with the conjugate by looping through vertices, edges, and faces in the primal arrangement and building associated dual vertices, edges, and fac...

The stochastic subgradient method is a widely used algorithm for solving large-scale optimization problems arising in machine learning. Often, these are neither smooth nor convex. Recently, Davis et al. , 2018 characterized the convergence of weakly convex case, which encompasses many important...

Proximal Markov chain Monte Carlo is a novel construct that lies at the intersection of Bayesian computation and convex optimization, which helped popularize use nondifferentiable priors in statistics. Existing formulations proximal MCMC, however, require hyperparameters regularization parameters to be prespecified. In this article, we extend paradigm MCMC through introducing new class called e...

We develop a connection between mixture and envelope representations of objective functions that arise frequently in statistics. We refer to this connection using the term “hierarchical duality.” Our results suggest an interesting and previously underexploited relationship between marginalization and profiling, or equivalently between the Fenchel–Moreau theorem for convex functions and the Bern...

The vaccine Bacillus of Calmette Guérin (BCG) was originally developed in France as an oral vaccine against tuberculosis. The oral use of this vaccine was replaced by the parenteral route in almost all countries after the Lubeck disaster. In contrast, Brazil retained the oral delivery of the vaccine until the mid-seventies when it was replaced by the intradermal route. This change in route of d...

In this paper, we attempt to investigate a class of constrained nonsmooth convex optimization problems, that is, piecewise C2 convex objectives with smooth convex inequality constraints. By using the Moreau-Yosida regularization, we convert these problems into unconstrained smooth convex programs. Then, we investigate the second-order properties of the Moreau-Yosida regularization η. By introdu...

regarding the role and importance of subsurface drainage in water table control, many studies have been made throughout the world to find out new techniques and more economical solutions, especially as related to different pipe envelope material and their installations. this research was conducted to investigate the use of rice husk, as drain envelope material, in drainage installations. in add...