Related papers: A Gradient-Based Implementation of the Polyhedral …

We consider problems with multiple linear objectives and linear constraints and use Adjustable Robust Optimization and Polynomial Optimization as tools to approximate the Pareto set with polynomials of arbitrarily large degree. The main…

This paper presents a deep machine learning architecture, the "polyharmonic cascade" -- a sequence of packages of polyharmonic splines, where each layer is rigorously derived from the theory of random functions and the principles of…

We prove that the active-set method needs an exponential number of iterations in the worst-case to maximize a convex quadratic function subject to linear constraints, regardless of the pivot rule used. This substantially improves over the…

This paper presents a practical GPU-accelerated convex hull algorithm and a novel Sorting-based Preprocessing Approach (SPA) for planar point sets. The proposed algorithm consists of two stages: (1) two rounds of preprocessing performed on…

Principal Component Analysis (PCA) is the workhorse tool for dimensionality reduction in this era of big data. While often overlooked, the purpose of PCA is not only to reduce data dimensionality, but also to yield features that are…

Stochastic approximation (SA) is a powerful class of iterative algorithms for nonlinear root-finding that can be used for minimizing a loss function, $L(\boldsymbol{\theta})$, with respect to a parameter vector $\boldsymbol{\theta}$, when…

We study synthetic aperture radar (SAR) imaging and motion estimation of complex scenes consisting of stationary and moving targets. We use the classic SAR setup with a single antenna emitting signals and receiving the echoes from the…

Convex polyhedra are the basis for several abstractions used in static analysis and computer-aided verification of complex and sometimes mission critical systems. For such applications, the identification of an appropriate…

In this work, we consider convex optimization problems with smooth objective function and nonsmooth functional constraints. We propose a new stochastic gradient algorithm, called Stochastic Halfspace Approximation Method (SHAM), to solve…

We present the last version of the PyrAmid Simulator Software for Adaptive opTics Arcetri (PASSATA), an IDL and CUDA based object oriented software developed in the Adaptive Optics group of the Arcetri observatory for Monte-Carlo end-to-end…

Due to their simplicity and excellent performance, parallel asynchronous variants of stochastic gradient descent have become popular methods to solve a wide range of large-scale optimization problems on multi-core architectures. Yet,…

This article describes a novel approach to chance-constrained programming based on the sample average approximation (SAA) method. Recent work focuses on heuristic approximations to the SAA problem and we introduce a novel approach which…

To leverage data and computation capabilities of mobile devices, machine learning algorithms are deployed at the network edge for training artificial intelligence (AI) models, resulting in the new paradigm of edge learning. In this paper,…

In 2019, Yoshida et al. developed tropical Principal Component Analysis (PCA), that is, an analogue of the classical PCA in the setting of tropical geometry and applied it to visualize a set of gene trees over a space of phylogenetic trees…

The multi-gradient descent algorithm (MGDA) finds a common descent direction that can improve all objectives by identifying the minimum-norm point in the convex hull of the objective gradients. This method has become a foundational tool in…

Tensor robust principal component analysis (TRPCA) has received a substantial amount of attention in various fields. Most existing methods, normally relying on tensor nuclear norm minimization, need to pay an expensive computational cost…

Expensive multi-objective optimization problems can be found in many real-world applications, where their objective function evaluations involve expensive computations or physical experiments. It is desirable to obtain an approximate Pareto…

In this paper we study feasibility and infeasibility of nonlinear two-stage fully adjustable robust feasibility problems with an empty first stage. This is equivalent to deciding whether the uncertainty set is contained within the…

Reliable uncertainty estimates are crucial for deploying pretrained models; yet, many strong methods for quantifying uncertainty require retraining, Monte Carlo sampling, or expensive second-order computations and may alter a frozen…

As AI-based applications become pervasive, CPU vendors are starting to incorporate matrix engines within the datapath to boost efficiency. Systolic arrays have been the premier architectural choice as matrix engines in offload accelerators.…