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Iterative methods are commonly used approaches to solve large, sparse linear systems, which are fundamental operations for many modern scientific simulations. When the large-scale iterative methods are running with a large number of ranks…
Given a connected, undirected graph whose edges are labelled (or coloured), the minimum labelling spanning tree (MLST) problem seeks a spanning tree whose edges have the smallest number of distinct labels (or colours). In recent work, the…
Overparameterization and overfitting are common concerns when designing and training deep neural networks, that are often counteracted by pruning and regularization strategies. However, these strategies remain secondary to most learning…
In low-dimensional topology, many important decision algorithms are based on normal surface enumeration, which is a form of vertex enumeration over a high-dimensional and highly degenerate polytope. Because this enumeration is subject to…
Dealing with multi-objective problems by using generation methods has some interesting advantages since it provides the decision-maker with the complete information about the set of non-dominated points (Pareto front) and a clear overview…
Multi-objective integer or mixed-integer programming problems typically have disconnected feasible domains, making the task of constructing an approximation of the Pareto front challenging. The present paper shows that certain algorithms…
Robust optimization provides a principled and unified framework to model many problems in modern operations research and computer science applications, such as risk measures minimization and adversarially robust machine learning. To use a…
We develop a backward-in-time machine learning algorithm that uses a sequence of neural networks to solve optimal switching problems in energy production, where electricity and fossil fuel prices are subject to stochastic jumps. We then…
Computing the coordinate-wise maxima of a planar point set is a classic and well-studied problem in computational geometry. We give an algorithm for this problem in the \emph{self-improving setting}. We have $n$ (unknown) independent…
We study the problem of solving linear program in the streaming model. Given a constraint matrix $A\in \mathbb{R}^{m\times n}$ and vectors $b\in \mathbb{R}^m, c\in \mathbb{R}^n$, we develop a space-efficient interior point method that…
We focus on modeling the relationship between an input feature vector and the predicted outcome of a trained decision tree using mixed-integer optimization. This can be used in many practical applications where a decision tree or tree…
Finding interactions between variables in large and high-dimensional datasets is often a serious computational challenge. Most approaches build up interaction sets incrementally, adding variables in a greedy fashion. The drawback is that…
Solving constrained nonlinear programs (NLPs) is of great importance in various domains such as power systems, robotics, and wireless communication networks. One widely used approach for addressing NLPs is the interior point method (IPM).…
Machine learning tasks are generally formulated as optimization problems, where one searches for an optimal function within a certain functional space. In practice, parameterized functional spaces are considered, in order to be able to…
We illustrate how computer-aided methods can be used to investigate the fundamental limits of the caching systems, which are significantly different from the conventional analytical approach usually seen in the information theory…
We introduce a class of "inverse parametric optimization" problems, in which one is given both a parametric optimization problem and a desired optimal solution; the task is to determine parameter values that lead to the given solution. We…
Symbolic indefinite integration in Computer Algebra Systems such as Maple involves selecting the most effective algorithm from multiple available methods. Not all methods will succeed for a given problem, and when several do, the results,…
An algorithm based on the interior-point methodology for solving continuous nonlinearly constrained optimization problems is proposed, analyzed, and tested. The distinguishing feature of the algorithm is that it presumes that only noisy…
Numerically locating the critical points of non-convex surfaces is a long-standing problem central to many fields. Recently, the loss surfaces of deep neural networks have been explored to gain insight into outstanding questions in…
We develop a new interior-point method (IPM) for symmetric-cone optimization, a common generalization of linear, second-order-cone, and semidefinite programming. In contrast to classical IPMs, we update iterates with a geodesic of the cone…