Related papers: On Reduction of Exhausters via a Support Function …
This paper provides a theoretical and numerical investigation of a penalty decomposition scheme for the solution of optimization problems with geometric constraints. In particular, we consider some situations where parts of the constraints…
This note deals with certain properties of convex functions. We provide results on the convexity of the set of minima of these functions, the behaviour of their subgradient set under restriction, and optimization of these functions over an…
Low-rank matrix completion consists of computing a matrix of minimal complexity that recovers a given set of observations as accurately as possible. Unfortunately, existing methods for matrix completion are heuristics that, while highly…
Compared to ordinary function minimization problems, min-max optimization algorithms encounter far greater challenges because of the existence of periodic cycles and similar phenomena. Even though some of these behaviors can be overcome in…
Motivated by resource allocation problems (RAPs) in power management applications, we investigate solutions to optimization problems that simultaneously minimize an entire class of objective functions. It is straightforward to show…
Upper semicontinuous (usc) functions arise in the analysis of maximization problems, distributionally robust optimization, and function identification, which includes many problems of nonparametric statistics. We establish that every usc…
Many high-dimensional optimisation problems exhibit rich geometric structures in their set of minimisers, often forming smooth manifolds due to over-parametrisation or symmetries. When this structure is known, at least locally, it can be…
Submodular functions are relevant to machine learning for at least two reasons: (1) some problems may be expressed directly as the optimization of submodular functions and (2) the lovasz extension of submodular functions provides a useful…
The various ways to reduce number of vectors describing condition of particles for high energy physics problems are presented. In particular decomposition of any vector with respect to the basis, consisting of any four linearly independent…
When constructing models of the world, we aim for optimal compressions: models that include as few details as possible while remaining as accurate as possible. But which details -- or features measured in data -- should we choose to include…
We introduce the cone of completely-positive functions, a subset of the cone of positive-type functions, and use it to fully characterize maximum-density distance-avoiding sets as the optimal solutions of a convex optimization problem. As a…
This tutorial summarizes recent advances in the convex relaxation of the optimal power flow (OPF) problem, focusing on structural properties rather than algorithms. Part I presents two power flow models, formulates OPF and their relaxations…
This work proposes an implementable proximal-type method for a broad class of optimization problems involving nonsmooth and nonconvex objective and constraint functions. In contrast to existing methods that rely on an ad hoc model…
The paper presents a topology optimization approach that designs an optimal structure, called a self-supporting structure, which is ready to be fabricated via additive manufacturing without the usage of additional support structures. Such…
We develop a technique for establishing lower bounds on the sample complexity of Least Squares (or, Empirical Risk Minimization) for large classes of functions. As an application, we settle an open problem regarding optimality of Least…
Cartoon-like images, i.e., C^2 functions which are smooth apart from a C^2 discontinuity curve, have by now become a standard model for measuring sparse (non-linear) approximation properties of directional representation systems. It was…
In information theory, some optimization problems result in convex optimization problems on strictly convex functionals of probability densities. In this note, we study these problems and show conditions of minimizers and the uniqueness of…
We identity the optimal non-infinitesimal direction of descent for a convex function. An algorithm is developed that can theoretically minimize a subset of (non-convex) functions.
This paper presents a kinematic definition of a serialized Stewart platform designed for autonomous in-space assembly called an Assembler. The Assemblers architecture describes problems inherent to the inverse kinematics of over-actuated…
In this note besides two abstract versions of the Vitali Covering Lemma an abstract Hardy-Littlewood Maximal Inequality, generalizing weak type (1,1) maximal function inequality, associated to any outer measure and a family of subsets on a…