Related papers: Non-uniform Grid Refinement for the Combinatorial …
A class of distributed optimization problem with a globally coupled equality constraint and local constrained sets is studied in this paper. For its special case where local constrained sets are absent, an augmented primal-dual gradient…
The stochastic gradient descent (SGD) algorithm has achieved remarkable success in training deep learning models. However, it has several limitations, including susceptibility to vanishing gradients, sensitivity to input data, and a lack of…
This work is devoted to the numerical simulation of nonlinear Schr\"odinger and Klein-Gordon equations. We present a general strategy to construct numerical schemes which are uniformly accurate with respect to the oscillation frequency.…
Quantum computing promises solutions to classically difficult and new-found problems through controlling the subtleties of quantum computing. The Quantum Approximate Optimisation Algorithm (QAOA) is a recently proposed quantum algorithm…
Subspace clustering (SC) is a popular method for dimensionality reduction of high-dimensional data, where it generalizes Principal Component Analysis (PCA). Recently, several methods have been proposed to enhance the robustness of PCA and…
We study the Regularized A-optimal Design (RAOD) problem, which selects a subset of $k$ experiments to minimize the inverse of the Fisher information matrix, regularized with a scaled identity matrix. RAOD has broad applications in Bayesian…
Sparse principal component analysis (PCA) and sparse canonical correlation analysis (CCA) are two essential techniques from high-dimensional statistics and machine learning for analyzing large-scale data. Both problems can be formulated as…
In this paper, we propose a framework based on the Retrospective Approximation (RA) paradigm to solve optimization problems with a stochastic objective function and general nonlinear deterministic constraints. This framework sequentially…
Variational quantum algorithms offer fascinating prospects for the solution of combinatorial optimization problems using digital quantum computers. However, the achievable performance in such algorithms and the role of quantum correlations…
Method for a mosaic image representation (MIR) is proposed for a selective treatment of image fragments of different transition frequency. MIR method is based on piecewise-constant image approximation on a non-uniform orthogonal grid…
In the present study, a numerical method, perturbation-iteration algorithm (shortly PIA), have been employed to give approximate solutions of nonlinear fractional-integro differential equations (FIDEs). Comparing with the exact solution,…
We study optimization methods for solving the maximum likelihood formulation of independent component analysis (ICA). We consider both the the problem constrained to white signals and the unconstrained problem. The Hessian of the objective…
Current methods for end-to-end constructive neural combinatorial optimization usually train a policy using behavior cloning from expert solutions or policy gradient methods from reinforcement learning. While behavior cloning is…
Decades of advances in mixed-integer linear programming (MILP) and recent development in mixed-integer second-order-cone programming (MISOCP) have translated very mildly to progresses in global solving nonconvex mixed-integer quadratically…
In this paper, we investigate a class of non-convex sum-of-ratios programs relevant to decision-making in key areas such as product assortment and pricing, and facility location and cost planning. These optimization problems, characterized…
Graph matching, typically formulated as a Quadratic Assignment Problem (QAP), seeks to establish node correspondences between two graphs. To address the NP-hardness of QAP, some existing methods adopt projection-based relaxations that embed…
Stochastic nonconvex optimization problems with nonlinear constraints have a broad range of applications in intelligent transportation, cyber-security, and smart grids. In this paper, first, we propose an inexact-proximal accelerated…
Model order reduction (MOR) techniques are often used to reduce the order of spatially-discretized (stochastic) partial differential equations and hence reduce computational complexity. A particular class of MOR techniques is balancing…
In container terminal yards, the Container Rehandling Problem (CRP) involves rearranging containers between stacks under specific operational rules, and it is a pivotal optimization challenge in intelligent container scheduling systems.…
Model predictive control problems for constrained hybrid systems are usually cast as mixed-integer optimization problems (MIP). However, commercial MIP solvers are designed to run on desktop computing platforms and are not suited for…