Related papers: Dual Hierarchical Least-Squares Programming with E…
Nonnegative (linear) least square problems are a fundamental class of problems that is well-studied in statistical learning and for which solvers have been implemented in many of the standard programming languages used within the machine…
We propose a new randomized algorithm for solving L2-regularized least-squares problems based on sketching. We consider two of the most popular random embeddings, namely, Gaussian embeddings and the Subsampled Randomized Hadamard Transform…
In this paper we present a novel numerical method for computing local minimizers of twice smooth differentiable non-linear programming (NLP) problems. So far all algorithms for NLP are based on either of the following three principles:…
We present a new class of decentralized first-order methods for nonsmooth and stochastic optimization problems defined over multiagent networks. Considering that communication is a major bottleneck in decentralized optimization, our main…
This paper introduces the distributed Halpern Peaceman--Rachford (dHPR) method, an efficient algorithm for solving distributed convex composite optimization problems with non-smooth objectives, which achieves a non-ergodic $O(1/k)$…
Solving linear programs is often a challenging task in distributed settings. While there are good algorithms for solving packing and covering linear programs in a distributed manner (Kuhn et al.~2006), this is essentially the only class of…
In this paper, a proximal augmented Lagrangian homotopy (PAL-Hom) method for solving convex quadratic programming problems is proposed. This method takes the proximal augmented Lagrangian method as the outer iteration. To solve the proximal…
Decentralized non-convex optimization is important in many problems of practical relevance. Existing decentralized methods, however, typically either lack convergence guarantees for general non-convex problems, or they suffer from a high…
All traditional methods of computing shortest paths depend upon edge-relaxation where the cost of reaching a vertex from a source vertex is possibly decreased if that edge is used. We introduce a method which maintains lower bounds as well…
Recent advances in operator learning have produced two distinct approaches for solving partial differential equations (PDEs): attention-based methods offering point-level adaptability but lacking spectral constraints, and spectral-based…
Support matrix machine (SMM) is an emerging classification framework that directly handles matrix-structured observations, thereby avoiding the spatial correlations destroyed by vectorization. However, most existing SMM variants rely on…
We study the bilinearly coupled minimax problem: $\min_{x} \max_{y} f(x) + y^\top A x - h(y)$, where $f$ and $h$ are both strongly convex smooth functions and admit first-order gradient oracles. Surprisingly, no known first-order algorithms…
The Hidden Subgroup Problem (HSP) is a computational problem which includes as special cases integer factorization, the discrete logarithm problem, graph isomorphism, and the shortest vector problem. The celebrated polynomial-time quantum…
Finding the solution to linear systems is at the heart of many applications in science and technology. Over the years a number of algorithms have been proposed to solve this problem on a digital quantum device, yet most of these are too…
Convex relaxation methods are powerful tools for studying the lowest energy of many-body problems. By relaxing the representability conditions for marginals to a set of local constraints, along with a global semidefinite constraint, a…
We present two parallel optimization algorithms for a convex function $f$. The first algorithm optimizes over linear inequality constraints in a Hilbert space, $\mathbb H$, and the second over a non convex polyhedron in $\mathbb R^n$. The…
We consider the least-squares approximation of a matrix C in the set of doubly stochastic matrices with the same sparsity pattern as C. Our approach is based on applying the well-known Alternating Direction Method of Multipliers (ADMM) to a…
We introduce a new fundamental algorithm called Matrix-POAFD to solve the matrix least square problem. The method is based on the matching pursuit principle. The method directly extracts, among the given features as column vectors of the…
Binary Neural Networks are a promising technique for implementing efficient deep models with reduced storage and computational requirements. The training of these is however, still a compute-intensive problem that grows drastically with the…
Solving large-scale multistage stochastic programming (MSP) problems poses a significant challenge as commonly used stagewise decomposition algorithms, including stochastic dual dynamic programming (SDDP), face growing time complexity as…