Related papers: Discrete Energy Minimization, beyond Submodularity…

The increasing penetration of distributed energy resources (DERs) brings opportunities and challenges to the operation of distribution systems. To ensure network integrity, dynamic operating envelopes (DOEs) are issued by utilities to DERs…

Many computer vision problems require optimization of binary non-submodular energies. We propose a general optimization framework based on local submodular approximations (LSA). Unlike standard LP relaxation methods that linearize the whole…

Optimization problems with both control variables and environmental variables arise in many fields. This paper introduces a framework of personalized optimization to han- dle such problems. Unlike traditional robust optimization,…

Subset selection tasks, arise in recommendation systems and search engines and ask to select a subset of items that maximize the value for the user. The values of subsets often display diminishing returns, and hence, submodular functions…

This article is devoted to one particular case of using universal accelerated proximal envelopes to obtain computationally efficient accelerated versions of methods used to solve various optimization problem setups. We propose a proximally…

This work addresses the challenge of minimizing the energy consumption of a wireless communication network by joint optimization of the base station transmit power and the cell activity. A mixed-integer nonlinear optimization problem is…

Submodularity is a key property in discrete optimization. Submodularity has been widely used for analyzing the greedy algorithm to give performance bounds and providing insight into the construction of valid inequalities for mixed-integer…

Recently a number of papers have suggested using neural-networks in order to approximate policy functions in DSGE models, while avoiding the curse of dimensionality, which for example arises when solving many HANK models, and while…

Over the past decade, deep learning models have exhibited considerable advancements, reaching or even exceeding human-level performance in a range of visual perception tasks. This remarkable progress has sparked interest in applying deep…

In this paper we study the fundamental problems of maximizing a continuous non-monotone submodular function over the hypercube, both with and without coordinate-wise concavity. This family of optimization problems has several applications…

We address the problem of minimal actuator placement in linear systems so that the volume of the set of states reachable with one unit or less of input energy is lower bounded by a desired value. First, following the recent work of…

We derive novel algorithms for optimization problems constrained by partial differential equations describing multiscale particle dynamics, including non-local integral terms representing interactions between particles. In particular, we…

Given the stringent requirements of energy efficiency for Internet-of-Things edge devices, approximate multipliers, as a basic component of many processors and accelerators, have been constantly proposed and studied for decades, especially…

In this paper we accomplish the development of the fast rank-adaptive solver for tensor-structured symmetric positive definite linear systems in higher dimensions. In [arXiv:1301.6068] this problem is approached by alternating minimization…

We present a practical and powerful new framework for both unconstrained and constrained submodular function optimization based on discrete semidifferentials (sub- and super-differentials). The resulting algorithms, which repeatedly compute…

In model selection problems for machine learning, the desire for a well-performing model with meaningful structure is typically expressed through a regularized optimization problem. In many scenarios, however, the meaningful structure is…

Binary optimization, a representative subclass of discrete optimization, plays an important role in mathematical optimization and has various applications in computer vision and machine learning. Usually, binary optimization problems are…

This thesis explores algorithmic applications and limitations of convex relaxation hierarchies for approximating some discrete and continuous optimization problems. - We show a dichotomy of approximability of constraint satisfaction…

Accurately solving PDEs with localised features requires refined meshes that adapt to the solution. Traditional numerical methods, such as finite elements, are linear in nature and often ineffective for such problems, as the mesh is not…

Optimization is fundamental in many areas of science, from computer science and information theory to engineering and statistical physics, as well as to biology or social sciences. It typically involves a large number of variables and a…