相关论文: An Efficient Unsupervised Framework for Convex Qua…

Convex quadratic programs (QPs) are fundamental to numerous applications, including finance, engineering, and energy systems. Among the various methods for solving them, the Douglas-Rachford (DR) splitting algorithm is notable for its…

Convex quadratic programming (QP) is an important class of optimization problem with wide applications in practice. The classic QP solvers are based on either simplex or barrier method, both of which suffer from the scalability issue…

Quadratically constrained quadratic programs (QCQPs) are ubiquitous in optimization: Such problems arise in applications from operations research, power systems, signal processing, chemical engineering, and portfolio theory, among others.…

We propose FlexQP, an always-feasible convex quadratic programming (QP) solver based on an $\ell_1$ elastic relaxation of the QP constraints. If the original constraints are feasible, FlexQP provably recovers the optimal solution. If the…

Convolutional Neural Networks (CNNs) are pivotal in computer vision and Big Data analytics but demand significant computational resources when trained on large-scale datasets. Conventional training via back-propagation (BP) with losses like…

Solving large-scale linear programming (LP) problems is an important task in various areas such as communication networks, power systems, finance and logistics. Recently, two distinct approaches have emerged to expedite LP solving: (i)…

Machine Learning (ML) optimization frameworks have gained attention for their ability to accelerate the optimization of large-scale Quadratically Constrained Quadratic Programs (QCQPs) by learning shared problem structures. However,…

Deep neural networks (DNNs) have been used to model complex optimization problems in many applications, yet have difficulty guaranteeing solution optimality and feasibility, despite training on large datasets. Training a NN as a surrogate…

Quadratic programming (QP) forms a crucial foundation in optimization, encompassing a broad spectrum of domains and serving as the basis for more advanced algorithms. Consequently, as the scale and complexity of modern applications continue…

Convex quadratic programs (QPs) constitute a fundamental computational primitive across diverse domains including financial optimization, control systems, and machine learning. The alternating direction method of multipliers (ADMM) has…

Data-driven decision-making processes increasingly utilize end-to-end learnable deep neural networks to render final decisions. Sometimes, the output of the forward functions in certain layers is determined by the solutions to mathematical…

Convex quadratic programming (QP) is an essential class of optimization problems with broad applications across various fields. Traditional QP solvers, typically based on simplex or barrier methods, face significant scalability challenges.…

We propose a solution approach for the problem (P) of minimizing an unconstrained binary polynomial optimization problem. We call this method PQCR (Polynomial Quadratic Convex Reformulation). The resolution is based on a 3-phase method. The…

We present new large-scale algorithms for fitting a subgradient regularized multivariate convex regression function to $n$ samples in $d$ dimensions -- a key problem in shape constrained nonparametric regression with applications in…

Quadratic programming (QP) is a fundamental optimization model with wide-ranging applications in decision-making and machine learning, yet efficiently solving large-scale instances remains a major computational challenge. Building upon the…

The linear primal-dual hybrid gradient (PDHG) method is a first-order method that splits convex optimization problems with saddle-point structure into smaller subproblems. Unlike those obtained in most splitting methods, these subproblems…

In wireless network, the optimization problems generally have complex constraints, and are usually solved via utilizing the traditional optimization methods that have high computational complexity and need to be executed repeatedly with the…

We introduce a cutting-plane framework for nonconvex quadratic programs (QPs) that progressively tightens convex relaxations. Our approach leverages the doubly nonnegative (DNN) relaxation to compute strong lower bounds and generate…

This paper presents a novel learning-based trajectory planning framework for quadrotors that combines model-based optimization techniques with deep learning. Specifically, we formulate the trajectory optimization problem as a quadratic…

Robust optimization has been established as a leading methodology to approach decision problems under uncertainty. To derive a robust optimization model, a central ingredient is to identify a suitable model for uncertainty, which is called…