Related papers: Progressive Convex Hull Simplification
We present an exact general remeshing scheme to compute analytic integrals of polynomial functions over the intersections between convex polyhedral cells of old and new meshes. In physics applications this allows one to ensure global mass,…
We study the problem of estimating the convex hull of the image $f(X)\subset\mathbb{R}^n$ of a compact set $X\subset\mathbb{R}^m$ with smooth boundary through a smooth function $f:\mathbb{R}^m\to\mathbb{R}^n$. Assuming that $f$ is a…
We study the convex hull membership (CHM) problem in the pure exploration setting where one aims to efficiently and accurately determine if a given point lies in the convex hull of means of a finite set of distributions. We give a complete…
A subgradient method is presented for solving general convex optimization problems, the main requirement being that a strictly-feasible point is known. A feasible sequence of iterates is generated, which converges to within user-specified…
In solving a multi-objective optimization problem by scalarization techniques, solutions to a scalarized problem are, in general, weakly efficient rather than efficient to the original problem. Thus, it is crucial to understand what problem…
Sampling biases in training data are a major source of algorithmic biases in machine learning systems. Although there are many methods that attempt to mitigate such algorithmic biases during training, the most direct and obvious way is…
Constant workspace algorithms use a constant number of words in addition to the read-only input to the algorithm. In this paper, we devise algorithms to efficiently compute relative hulls in the plane using a constant workspace.…
In this paper we develop proximal methods for statistical learning. Proximal point algorithms are useful in statistics and machine learning for obtaining optimization solutions for composite functions. Our approach exploits closed-form…
We describe an algorithm for computing the convex hull of a finite collection of points in the affine building of SL_d(K), for K a field with discrete valuation. These convex hulls describe the relations among a finite collection of…
The pooling problem is a classical NP-hard problem in the chemical process and petroleum industries. This problem is modeled as a nonlinear, nonconvex network flow problem in which raw materials with different specifications are blended in…
Direct search is one of the most popular derivative-free optimization paradigms, that relies on exploring the variable space using polling directions. To analyze and implement direct search, one typically relies on positive spanning sets.…
Efficient representations of convex sets are of crucial importance for many algorithms that work with them. It is well-known that sometimes, a complicated convex set can be expressed as the projection of a much simpler set in higher…
In this paper we derive strong linear inequalities for sets of the form {(x, q) \in Rd \times R : q \geq Q(x), x \in Rd - int(P)}, where Q(x) : Rd \rightarrow R is a quadratic function, P \subset Rd and "int" denotes interior. Of particular…
In this paper, we consider the problem of covering a plane region with unit discs. We present an improved upper bound and the first nontrivial lower bound on the number of discs needed for such a covering, depending on the area and…
We present two parallel optimization algorithms for a convex function $f$. The first algorithm optimizes over linear inequality constraints in a Hilbert space, $\mathbb H$, and the second over a non convex polyhedron in $\mathbb R^n$. The…
We present new algorithms to perform fast probabilistic collision queries between convex as well as non-convex objects. Our approach is applicable to general shapes, where one or more objects are represented using Gaussian probability…
We propose several new nonsmooth Newton methods for solving convex composite optimization problems with polyhedral regularizers, while avoiding the computation of complicated second-order information on these functions. Under the…
Piecewise linear vector optimization problems in a locally convex Hausdorff topological vector spaces setting are considered in this paper. The efficient solution set of these problems are shown to be the unions of finitely many semi-closed…
Traditional algorithms for stochastic optimization require projecting the solution at each iteration into a given domain to ensure its feasibility. When facing complex domains, such as positive semi-definite cones, the projection operation…
This article focuses on numerical efficiency of projection algorithms for solving linear optimization problems. The theoretical foundation for this approach is provided by the basic result that bounded finite dimensional linear optimization…