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The forward-backward splitting technique is a popular method for solving monotone inclusions that has applications in optimization. In this paper we explore the behaviour of the algorithm when the inclusion problem has no solution. We…

This paper is concerned with a blood flow problem coupled with a slow plaque growth at the artery wall. In the model, the micro (fast) system is the Navier-Stokes equation with a periodically applied force and the macro (slow) system is a…

Lower-bound analyses for nonconvex strongly-concave minimax optimization problems have shown that stochastic first-order algorithms require at least $\mathcal{O}(\varepsilon^{-4})$ oracle complexity to find an $\varepsilon$-stationary…

We introduce and investigate the convergence properties of an inertial forward-backward-forward splitting algorithm for approaching the set of zeros of the sum of a maximally monotone operator and a single-valued monotone and Lipschitzian…

We consider a mixed variational formulation recently proposed for the coupling of the Brinkman--Forchheimer and Darcy equations and develop the first reliable and efficient residual-based a posteriori error estimator for the 2D version of…

Solving high-dimensional Fokker-Planck (FP) equations is a challenge in computational physics and stochastic dynamics, due to the curse of dimensionality (CoD) and unbounded domains. Existing deep learning approaches, such as…

In this paper we propose an efficient distributed algorithm for solving loosely coupled convex optimization problems. The algorithm is based on a primal-dual interior-point method in which we use the alternating direction method of…

The forward-backward operator splitting algorithm is one of the most important methods for solving the optimization problem of the sum of two convex functions, where one is differentiable with a Lipschitz continuous gradient and the other…

Accurate prediction of rarefied gas flows is important for space vehicle design, particularly in rarefied regimes where the Navier-Stokes equations are no more valid. While the direct simulation Monte Carlo (DSMC) method acts as a numerical…

Recent work on approximate linear programming (ALP) techniques for first-order Markov Decision Processes (FOMDPs) represents the value function linearly w.r.t. a set of first-order basis functions and uses linear programming techniques to…

We discretize the Lagrange multiplier formulation of the obstacle problem by mixed and stabilized finite element methods. A priori and a posteriori error estimates are derived and numerically verified.

First we show that physics-informed neural networks are not suitable for a large class of parabolic partial differential equations including the Fokker-Planck equation. Then we devise an algorithm to compute solutions of the Fokker-Planck…

This paper proposes a set of novel optimization algorithms for solving a class of convex optimization problems with time-varying streaming cost function. We develop an approach to track the optimal solution with a bounded error. Unlike the…

Selecting the fastest algorithm for a specific signal/image processing task is a challenging question. We propose an approach based on the Performance Estimation Problem framework that numerically and automatically computes the worst-case…

This paper improves the state-of-the-art rate of a first-order algorithm for solving entropy regularized optimal transport. The resulting rate for approximating the optimal transport (OT) has been improved from…

Consider the problem of minimizing the expected value of a (possibly nonconvex) cost function parameterized by a random (vector) variable, when the expectation cannot be computed accurately (e.g., because the statistics of the random…

We give new approximation algorithms for the submodular joint replenishment problem and the inventory routing problem, using an iterative rounding approach. In both problems, we are given a set of $N$ items and a discrete time horizon of…

We propose a variant of the Frank-Wolfe algorithm for solving a class of sparse/low-rank optimization problems. Our formulation includes Elastic Net, regularized SVMs and phase retrieval as special cases. The proposed Primal-Dual Block…

Constrained non-convex optimization problems frequently arise in control applications. Solving such problems is inherently challenging, as existing methods often converge to suboptimal local minima or incur prohibitive computational costs.…

We propose a new speed and departure time optimization algorithm for the Pollution-Routing Problem (PRP), which runs in quadratic time and returns a certified optimal schedule. This algorithm is embedded into an iterated local search-based…