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We introduce the Stochastic Asynchronous Proximal Alternating Linearized Minimization (SAPALM) method, a block coordinate stochastic proximal-gradient method for solving nonconvex, nonsmooth optimization problems. SAPALM is the first asynchronous parallel optimization method that provably converges on a large class of nonconvex, nonsmooth problems. We prove(More)
This paper describes Convex, a convex optimization modeling framework in Julia. Convex translates problems from a user-friendly functional language into an abstract syntax tree describing the problem. This concise representation of the global structure of the problem allows Convex to infer whether the problem complies with the rules of disciplined convex(More)
Principal components analysis (PCA) is a well-known technique for approximating a data set represented by a matrix by a low rank matrix. Here, we extend the idea of PCA to handle arbitrary data sets consisting of numerical, Boolean, categorical, ordinal, and other data types. This framework encompasses many well known techniques in data analysis, such as(More)
The problem of maximizing a sum of sigmoidal functions over a convex constraint set arises in many application areas. This objective captures the idea of decreasing marginal returns to investment, and has applications in mathematical marketing, network bandwidth allocation, revenue optimization, optimal bidding, and lottery design. We define the sigmoidal(More)
We present two modifications of the flux balance analysis (FBA) metabolic modeling framework which relax implicit assumptions of the biomass reaction. Our flexible flux balance analysis (flexFBA) objective removes the fixed proportion between reactants, and can therefore produce a subset of biomass reactants. Our time-linked flux balance analysis (tFBA)(More)
We consider the problem of learning the preferences of a heterogeneous population by observing choices from an assortment of products, ads, or other offerings. Our observation model takes a form common in assortment planning applications: each arriving customer is offered an assortment consisting of a subset of all possible offerings; we observe only the(More)
We consider the problem of minimizing a sum of non-convex functions over a compact domain, subject to linear inequality and equality constraints. Approximate solutions can be found by solving a convex-ified version of the problem, in which each function in the objective is replaced by its convex envelope. We propose a randomized algorithm to solve the(More)