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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…
New iterative methods for solving linear equations are presented that are easy to use, generalize good existing methods, and appear to be faster. The new algorithms mix two kinds of linear recurrence formulas. Older methods have either high…
We present a matrix-factorization algorithm that scales to input matrices with both huge number of rows and columns. Learned factors may be sparse or dense and/or non-negative, which makes our algorithm suitable for dictionary learning,…
We propose general notions to deal with large scale polynomial optimization problems and demonstrate their efficiency on a key industrial problem of the twenty first century, namely the optimal power flow problem. These notions enable us to…
In this paper we present a new algorithmic realization of a projection-based scheme for general convex constrained optimization problem. The general idea is to transform the original optimization problem to a sequence of feasibility…
Execution graphs of parallel loop programs exhibit a nested, repeating structure. We show how such graphs that are the result of nested repetition can be represented by succinct parametric structures. This parametric graph template…
We apply a reinforcement learning algorithm to show how smart particles can learn approximately optimal strategies to navigate in complex flows. In this paper we consider microswimmers in a paradigmatic three-dimensional case given by a…
Reducing the conditions under which a given set satisfies the stipulations of the subset sum proposition to a set of linear relationships, the question of whether a set satisfies subset sum may be answered in a polynomial number of steps by…
In many power system optimization problems, we observe that only a small fraction of the line flow constraints ever become active at the optimal solution, despite variations in the load profile and generation costs. This observation has…
Accelerated gradient descent iterations are widely used in optimization. It is known that, in the continuous-time limit, these iterations converge to a second-order differential equation which we refer to as the accelerated gradient flow.…
We study a graph partitioning problem motivated by the simulation of the physical movement of multi-body systems on an atomistic level, where the forces are calculated from a quantum mechanical description of the electrons. Several advanced…
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…
This paper considers an optimization problem for a dynamical system whose evolution depends on a collection of binary decision variables. We develop scalable approximation algorithms with provable suboptimality bounds to provide…
The method of extremal flows has presented an alluring alternative approach to numerically solving bootstrap constraints. Here I present the development and adaptation of that approach to a more general class of flows with apparent…
Motivated by the grid search method and Bayesian optimization, we introduce the concept of contractibility and its applications in model-based optimization. First, a basic framework of contraction methods is established to construct a…
The pooling problem has applications, e.g., in petrochemical refining, water networks, and supply chains and is widely studied in global optimization. To date, it has largely been treated deterministically, neglecting the influence of…
We present a matrix factorization algorithm that scales to input matrices that are large in both dimensions (i.e., that contains morethan 1TB of data). The algorithm streams the matrix columns while subsampling them, resulting in low…
A finite element method for solving nonlinear differential equations on a grid, with potential applicability to computational fluid dynamics (CFD), is developed and tested. The current method facilitates the computation of solutions of a…
The works presented in this habilitation concern the algorithmics of polynomials. This is a central topic in computer algebra, with numerous applications both within and outside the field - cryptography, error-correcting codes, etc. For…
This paper studies first-order algorithms for solving fully composite optimization problems over convex and compact sets. We leverage the structure of the objective by handling its differentiable and non-differentiable components…