Related papers: Tuning Multigrid Methods with Robust Optimization
We present a multi-level graph partitioning algorithm using novel local improvement algorithms and global search strategies transferred from the multi-grid community. Local improvement algorithms are based max-flow min-cut computations and…
We present a complete classification of the distributed computational complexity of local optimization problems in directed cycles for both the deterministic and the randomized LOCAL model. We show that for any local optimization problem…
Partial-differential-equation (PDE)-constrained optimization is a well-worn technique for acquiring optimal parameters of systems governed by PDEs. However, this approach is limited to providing a single set of optimal parameters per…
Recently, convex formulations of low-rank matrix factorization problems have received considerable attention in machine learning. However, such formulations often require solving for a matrix of the size of the data matrix, making it…
Minimax optimization has found extensive applications in modern machine learning, in settings such as generative adversarial networks (GANs), adversarial training and multi-agent reinforcement learning. As most of these applications involve…
When approaching a clustering problem, choosing the right clustering algorithm and parameters is essential, as each clustering algorithm is proficient at finding clusters of a particular nature. Due to the unsupervised nature of clustering…
We study the parameterized complexity of a broad class of problems called "local graph partitioning problems" that includes the classical fixed cardinality problems as max k-vertex cover, k-densest subgraph, etc. By developing a technique…
One way to analyze Cyber-Physical Systems is by modeling them as hybrid automata. Since reachability analysis for hybrid nonlinear automata is a very challenging and computationally expensive problem, in practice, engineers try to solve the…
Discrete-time robust optimal control problems generally take a min-max structure over continuous variable spaces, which can be difficult to solve in practice. In this paper, we extend the class of such problems that can be solved through a…
In super-resolution it is necessary to locate with high precision point sources from noisy observations of the spectrum of the signal at low frequencies capped by f_c. In the case when the point sources are positive and are located on a…
We develop and analyze a set of new sequential simulation-optimization algorithms for large-scale multi-dimensional discrete optimization via simulation problems with a convexity structure. The "large-scale" notion refers to that the…
Optimization problems with both control variables and environmental variables arise in many fields. This paper introduces a framework of personalized optimization to han- dle such problems. Unlike traditional robust optimization,…
Traditional deep network training methods optimize a monolithic objective function jointly for all the components. This can lead to various inefficiencies in terms of potential parallelization. Local learning is an approach to…
Sparse principal component analysis addresses the problem of finding a linear combination of the variables in a given data set with a sparse coefficients vector that maximizes the variability of the data. This model enhances the ability to…
Fourier-encoded implicit neural representations (INRs) have shown strong capability in modeling continuous signals from discrete samples. However, conventional Fourier feature mappings use a fixed set of frequencies over the entire spatial…
An algorithm which computes a solution of a set optimization problem is provided. The graph of the objective map is assumed to be given by finitely many linear inequalities. A solution is understood to be a set of points in the domain…
We introduce a new and increasingly relevant setting for distributed optimization in machine learning, where the data defining the optimization are unevenly distributed over an extremely large number of nodes. The goal is to train a…
Necessary optimality conditions in Lagrangian form and the sequential minimization framework are extended to mixed-integer nonlinear optimization, without any convexity assumptions. Building upon a recently developed notion of local…
Our research deals with the optimization version of the set partition problem, where the objective is to minimize the absolute difference between the sums of the two disjoint partitions. Although this problem is known to be NP-hard and…
We present algorithms for efficiently learning regularizers that improve generalization. Our approach is based on the insight that regularizers can be viewed as upper bounds on the generalization gap, and that reducing the slack in the…