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A linear program with linear complementarity constraints (LPCC) requires the minimization of a linear objective over a set of linear constraints together with additional linear complementarity constraints. This class has emerged as a…
We develop a new numerical method for approximating the infinite time reachable set of strictly stable linear control systems. By solving a linear program with a constraint that incorporates the system dynamics, we compute a polytope with…
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…
We propose an implementable, neural network-based structure preserving probabilistic numerical approximation for a generalized obstacle problem describing the value of a zero-sum differential game of optimal stopping with asymmetric…
This paper offers a contemporary and comprehensive perspective on the classical algorithms utilized for the solution of minimum-time problem for linear systems (MTPLS). The use of unified notations supported by visual geometric…
We propose a novel stochastic distributed method for both monotone and strongly monotone variational inequalities with Lipschitz operator and proper convex regularizers arising in various applications from game theory to adversarial…
The multireference alignment problem consists of estimating a signal from multiple noisy shifted observations. Inspired by existing Unique-Games approximation algorithms, we provide a semidefinite program (SDP) based relaxation which…
This paper investigates repeated win-lose coordination games (WLC-games). We analyse which protocols are optimal for these games covering both the worst case and average case scenarios, i,e., optimizing the guaranteed and expected…
We consider a system of nonlinear ordinary differential equations for the solution of linear programming (LP) problems that was first proposed in the mathematical biology literature as a model for the foraging behavior of acellular slime…
This article presents a numerical illustration of a recently proposed strongly polynomial-time algorithm for the general linear programming (LP) problem. Each iteration of the proposed algorithm consists of two Gauss-Jordan pivoting…
The paper aims at the development of an apparatus for analysis and construction of near optimal solutions of singularly perturbed (SP) optimal controls problems (that is, problems of optimal control of SP systems) considered on the infinite…
This paper investigates repeated win-lose coordination games (WLC-games). We analyse which protocols are optimal for these games, covering both the worst case and average case scenarios, i,e., optimizing the guaranteed and expected…
We develop a polynomial time $\Omega\left ( \frac 1R \log R \right)$ approximate algorithm for Max 2CSP-$R$, the problem where we are given a collection of constraints, each involving two variables, where each variable ranges over a set of…
Change-point problems have appeared in a great many applications for example cancer genetics, econometrics and climate change. Modern multiscale type segmentation methods are considered to be a statistically efficient approach for multiple…
We consider large linear and nonlinear fixed point problems, and solution with proximal algorithms. We show that there is a close connection between two seemingly different types of methods from distinct fields: 1) Proximal iterations for…
Finding a stable matching is one of the central problems in algorithmic game theory. If participants are allowed to have ties and incomplete preferences, computing a stable matching of maximum cardinality is known to be NP-hard. In this…
Gaussian processes (GP) are one of the most successful frameworks to model uncertainty. However, GP optimization (e.g., GP-UCB) suffers from major scalability issues. Experimental time grows linearly with the number of evaluations, unless…
I adapt Berlekamp's light bulb switching game to finite projective plans and finite affine planes, then find the worst arrangement of lit bulbs for planes of even and odd orders. The results are then extended from the planes to spaces of…
We consider a natural generalization of scheduling $n$ jobs on $m$ parallel machines so as to minimize the makespan. In our extension the set of jobs is partitioned into several classes and a machine requires a setup whenever it switches…
This paper considers a general class of iterative optimization algorithms, referred to as linear-optimization-based convex programming (LCP) methods, for solving large-scale convex programming (CP) problems. The LCP methods, covering the…