We study algebraic properties of cost functions. We give an application: building sets close to being Turing complete.

In PODS 2003, Babcock, Datar, Motwani and O’Callaghan [4] gave the first streaming solution for the k-median problem on sliding windows using O( k τ4W 2τ log2 W ) space, with a O(2O(1/τ)) approximation factor, where W is the window size and τ ∈ (0, 2 ) is a user-specified parameter. They left as an open question whether it is possible to improve this to polylogarithmic space. Despite much progr...

The concept of Support Vector Regression is extended to a more general class of convex cost functions. It is shown how the resulting convex constrained optimization problems can be eeciently solved by a Primal{Dual Interior Point path following method. Both computational feasibility and improvement of estimation is demonstrated in the experiments.

Regular cost functions were introduced as a quantitative generalisation of regular languages, retaining many of their equivalent characterisations and decidability properties. For instance, stabilisation monoids play the same role for cost functions as monoids do for regular languages. The purpose of this article is to further extend this algebraic approach by generalizing two results on regula...

We give a necessary and sufficient condition on the cost function so that the map solution of Monge’s optimal transportation problem is continuous for arbitrary smooth positive data. This condition was first introduced by Ma, Trudinger and Wang [17, 21] for a priori estimates of the corresponding Monge-Ampère equation. It is expressed by a socalled cost-sectional curvature being non-negative. W...

The purpose of this work is to develop and study a decentralized strategy for Pareto optimization an aggregate cost consisting regularized risks. Each risk modeled as the expectation some loss function with unknown probability distribution while regularizers are assumed deterministic, but not required be differentiable or even continuous. individual, regularized, functions distributed across st...

Introduction This paper describes the application of Newton Method for solving strictly convex separable network quadratic programs. The authors provide a brief synopsis of separable network quadratic programming and list the various techniques for solving the same. The main thrust of the paper is succinctly identified by the following: 1. Providing a generic subroutine that can be used by vari...

Constructing accurate and generalizable approximators (surrogate models) for complex physico-chemical processes exhibiting highly non-smooth dynamics is challenging. The main question what type of surrogate models we should construct these be under-parameterized or over-parameterized. In this work, propose new developments perform comparisons two promising approaches: manifold-based polynomial ...