Related papers: Entropy linear programming
Linear Programming (LP) is a foundational optimization technique with widespread applications in finance, energy trading, and supply chain logistics. However, traditional Central Processing Unit (CPU)-based LP solvers often struggle to meet…
We propose new linear combinations of compositions of a basic second-order scheme with appropriately chosen coefficients to construct higher order numerical integrators for differential equations. They can be considered as a generalization…
This paper investigates the deep learning optimization problem with softmax cross-entropy loss. We propose a layer separation strategy to alleviate the strong nonconvexity encountered during training deep networks. For cross-entropy models…
This paper studies the equitable and optimal transport (EOT) problem, which has many applications such as fair division problems and optimal transport with multiple agents etc. In the discrete distributions case, the EOT problem can be…
We propose a novel iterative algorithm for solving a large sparse linear system. The method is based on the EM algorithm. If the system has a unique solution, the algorithm guarantees convergence with a geometric rate. Otherwise,…
We present a distributed framework of the Primal-Dual Hybrid Gradient (PDHG) algorithm for solving massive-scale linear programming (LP) problems. Although PDHG-based solvers demonstrate strong performance on single-node GPU architectures,…
In this paper, we introduce two parallel extragradient-proximal methods for solving split equilibrium problems. The algorithms combine the extragradient method, the proximal method and the hybrid (outer approximation) method. The weak and…
While deep neural networks are highly effective at solving complex tasks, large pre-trained models are commonly employed even to solve consistently simpler downstream tasks, which do not necessarily require a large model's complexity.…
This paper introduces a new method of partitioning the solution space of a multi-objective optimisation problem for parallel processing, called Efficient Projection Partitioning. This method projects solutions down into a single dimension,…
We consider stochastic gradient methods under the interpolation regime where a perfect fit can be obtained (minimum loss at each observation). While previous work highlighted the implicit regularization of such algorithms, we consider an…
The objective of drug discovery is to identify chemical compounds that possess specific pharmaceutical properties toward a binding target. Existing large language models (LLMS) can achieve high token matching scores in terms of likelihood…
Traditionally, there are several polynomial algorithms for linear programming including the ellipsoid method, the interior point method and other variants. Recently, Chubanov [Chubanov, 2015] proposed a projection and rescaling algorithm,…
In this paper, we consider the problem of $\ell_{p}$ norm linear regression, which has several applications such as in sparse recovery, data clustering, and semi-supervised learning. The problem, even though convex, does not enjoy a…
A new fast multipole formulation for solving elliptic difference equations on unbounded domains and its parallel implementation are presented. These difference equations can arise directly in the description of physical systems, e.g.…
In this paper we introduce a generic model for multiplicative algorithms which is suitable for the MapReduce parallel programming paradigm. We implement three typical machine learning algorithms to demonstrate how similarity comparison,…
In this paper, a new iterative two-level algorithm is presented for solving the finite element discretization for nonsymmetric or indefinite elliptic problems. The iterative two-level algorithm uses the same coarse space as the traditional…
The Extreme Learning Machine (ELM) is a growing statistical technique widely applied to regression problems. In essence, ELMs are single-layer neural networks where the hidden layer weights are randomly sampled from a specific distribution,…
A numerical method is developed to solve linear semi-infinite programming problem (LSIP) in which the iterates produced by the algorithm are feasible for the original problem. This is achieved by constructing a sequence of standard linear…
The continuous nonlinear resource allocation problem (CONRAP) has broad applications in economics, engineering, production and inventory management, and often serves as a subproblem in complex programming. Without relying on monotonicity…
In real-world applications, it is important for machine learning algorithms to be robust against data outliers or corruptions. In this paper, we focus on improving the robustness of a large class of learning algorithms that are formulated…