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Sparse optimization is a central problem in machine learning and computer vision. However, this problem is inherently NP-hard and thus difficult to solve in general. Combinatorial search methods find the global optimal solution but are…
There has been a recent interest in understanding the power of local algorithms for optimization and inference problems on sparse graphs. Gamarnik and Sudan (2014) showed that local algorithms are weaker than global algorithms for finding…
We present a novel approach for constructing discrete optimization benchmarks that enables fine-grained control over problem properties, and such benchmarks can facilitate analyzing discrete algorithm behaviors. We build benchmark problems…
The recently developed Distributed Block Proximal Method, for solving stochastic big-data convex optimization problems, is studied in this paper under the assumption of constant stepsizes and strongly convex (possibly non-smooth) local…
Five ordering algorithms for the nonserial dynamic programming algorithm for solving sparse discrete optimization problems are compared in this paper. The benchmarking reveals that the ordering of the variables has a significant impact on…
Multistage stochastic optimization problems are, by essence, complex as their solutions are indexed both by stages and by uncertainties. Their large scale nature makes decomposition methods appealing, like dynamic programming which is a…
Wall-clock-time is minimized for a solution to a linear-program with block-diagonal-structure, by decomposing the linear-program into as many small-sized subproblems as possible, each block resulting in a separate subproblem, when the…
Compressing resource-intensive large language models by removing whole transformer blocks is a seemingly simple idea, but identifying which blocks to remove constitutes an exponentially difficult combinatorial problem. In this paper, we…
We consider a discrete optimization formulation for learning sparse classifiers, where the outcome depends upon a linear combination of a small subset of features. Recent work has shown that mixed integer programming (MIP) can be used to…
We propose a new algorithm to solve sparse linear systems of equations over the integers. This algorithm is based on a $p$-adic lifting technique combined with the use of block matrices with structured blocks. It achieves a sub-cubic…
The numerical realization of the dynamic programming principle for continuous-time optimal control leads to nonlinear Hamilton-Jacobi-Bellman equations which require the minimization of a nonlinear mapping over the set of admissible…
We study the optimization version of the set partition problem (where the difference between the partition sums are minimized), which has numerous applications in decision theory literature. While the set partitioning problem is NP-hard and…
Packing and covering semidefinite programs (SDPs) appear in natural relaxations of many combinatorial optimization problems as well as a number of other applications. Recently, several techniques were proposed, that utilize the particular…
Linear discriminant analysis (LDA) is a classical method for dimensionality reduction, where discriminant vectors are sought to project data to a lower dimensional space for optimal separability of classes. Several recent papers have…
Topology optimization problems often support multiple local minima due to a lack of convexity. Typically, gradient-based techniques combined with continuation in model parameters are used to promote convergence to more optimal solutions;…
In this article the most fundamental decomposition-based optimization method - block coordinate search, based on the sequential decomposition of problems in subproblems - and building performance simulation programs are used to reason about…
In symmetric block eigenvalue algorithms, such as the subspace iteration algorithm and the locally optimal block preconditioned conjugate gradient (LOBPCG) algorithm, a large block size is often employed to achieve robustness and rapid…
Iterative methods for solving large sparse systems of linear equations are widely used in many HPC applications. Extreme scaling of these methods can be difficult, however, since global communication to form dot products is typically…
Finding sparse solutions of underdetermined systems of linear equations is a fundamental problem in signal processing and statistics which has become a subject of interest in recent years. In general, these systems have infinitely many…
A class of splitting alternating algorithms is proposed for finding the sparse solution of linear systems with concatenated orthogonal matrices. Depending on the number of matrices concatenated, the proposed algorithms are classified into…