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We consider continuous-time dynamics for distributed optimization with set constraints in the paper. To handle the computational complexity of projection-based dynamics due to solving a general quadratic optimization subproblem with…
We propose an algorithm to compute the dynamics of articulated rigid-bodies with different sensor distributions. Prior to the on-line computations, the proposed algorithm performs an off-line optimisation step to simplify the computational…
The discrete Wasserstein barycenter problem is a minimum-cost mass transport problem for a set of discrete probability measures. Although an exact barycenter is computable through linear programming, the underlying linear program can be…
Linear optimal power flow (LOPF) algorithms use a linearization of the alternating current (AC) load flow equations to optimize generator dispatch in a network subject to the loading constraints of the network branches. Common algorithms…
We propose an algorithm which appears to be the first bridge between the fields of conditional gradient methods and abs-smooth optimization. Our problem setting is motivated by various applications that lead to nonsmoothness, such as…
We demonstrate that valid inequalities, or lifted nonlinear cuts (LNC), can be projected to tighten the Second Order Cone (SOC), Convex DistFlow (CDF), and Network Flow (NF) relaxations of the AC Optimal Power Flow (AC-OPF) problem. We…
The boosted Frank-Wolfe algorithm accelerates the classical Frank-Wolfe algorithm by better aligning the update direction with the negative gradient. Its analysis, however, has been limited to deterministic convex problems, with step sizes…
We develop a Frank-Wolfe algorithm with corrective steps, generalizing previous algorithms including blended conditional gradients, blended pairwise conditional gradients, and fully-corrective Frank-Wolfe. For this, we prove tight…
Score-based or diffusion models generate high-quality tabular data, surpassing GAN-based and VAE-based models. However, these methods require substantial training time. In this paper, we introduce RecTable, which uses the rectified flow…
We consider a class of linear-programming based estimators in reconstructing a sparse signal from linear measurements. Specific formulations of the reconstruction problem considered here include Dantzig selector, basis pursuit (for the case…
Neural networks have been successfully applied in various resource-constrained edge devices, where usually central processing units (CPUs) instead of graphics processing units exist due to limited power availability. State-of-the-art…
Frank-Wolfe (FW) algorithms have emerged as an essential class of methods for constrained optimization, especially on large-scale problems. In this paper, we summarize the algorithmic design choices and progress made in the last years of…
Recently, there has been a renewed interest in the machine learning community for variants of a sparse greedy approximation procedure for concave optimization known as {the Frank-Wolfe (FW) method}. In particular, this procedure has been…
While researchers in the asset management industry have mostly focused on techniques based on financial and risk planning techniques like Markowitz efficient frontier, minimum variance, maximum diversification or equal risk parity, in…
Image fusion is a fundamental and important task in computer vision, aiming to combine complementary information from different modalities to fuse images. In recent years, diffusion models have made significant developments in the field of…
The study of high-dimensional differential equations is challenging and difficult due to the analytical and computational intractability. Here, we improve the speed of waveform relaxation (WR), a method to simulate high-dimensional…
Machine learning techniques, in particular the so-called normalizing flows, are becoming increasingly popular in the context of Monte Carlo simulations as they can effectively approximate target probability distributions. In the case of…
The classical alternating current optimal power flow problem is highly nonconvex and generally hard to solve. Convex relaxations, in particular semidefinite, second-order cone, convex quadratic, and linear relaxations, have recently…
We present rectified flow, a surprisingly simple approach to learning (neural) ordinary differential equation (ODE) models to transport between two empirically observed distributions \pi_0 and \pi_1, hence providing a unified solution to…
Faced with saturation of Moore's law and increasing dimension of data, system designers have increasingly resorted to parallel and distributed computing. However, distributed computing is often bottle necked by a small fraction of slow…