相关论文: Modified limited memory BFGS with displacement agg…

In this paper, we consider nonconvex minimax optimization, which is gaining prominence in many modern machine learning applications such as GANs. Large-scale edge-based collection of training data in these applications calls for…

Wave equation techniques have been an integral part of geophysical imaging workflows to investigate the Earth's subsurface. Least-squares reverse time migration (LSRTM) is a linearized inversion problem that iteratively minimizes a misfit…

We present an alternating augmented Lagrangian method for convex optimization problems where the cost function is the sum of two terms, one that is separable in the variable blocks, and a second that is separable in the difference between…

While convergence of the Alternating Direction Method of Multipliers (ADMM) on convex problems is well studied, convergence on nonconvex problems is only partially understood. In this paper, we consider the Gaussian phase retrieval problem,…

In this paper, a stochastic alternating direction method of multipliers (ADMM) is proposed for a class of nonsmooth composite and stochastic convex optimization problems in Hilbert space, motivated by optimization problems constrained by…

Latent Gaussian models (LGMs) are widely used in statistics and machine learning. Bayesian inference in non-conjugate LGMs is difficult due to intractable integrals involving the Gaussian prior and non-conjugate likelihoods. Algorithms…

Quasi-Newton methods still face significant challenges in training large-scale neural networks due to additional compute costs in the Hessian related computations and instability issues in stochastic training. A well-known method, L-BFGS…

We present a novel efficient theoretical and numerical framework for solving global non-convex polynomial optimization problems. We analytically demonstrate that such problems can be efficiently reformulated using a non-linear objective…

Binary tomography is concerned with reconstructing a binary image from a very small number or other limited CT projection data. This problem itself not only possesses several medical imaging applications but also can be considered a model…

The linearly constrained convex composite programming problems whose objective function contains two blocks with each block being the form of nonsmooth+smooth arises frequently in multiple fields of applications. If both of the smooth terms…

Unsupervised feature selection has drawn wide attention in the era of big data since it is a primary technique for dimensionality reduction. However, many existing unsupervised feature selection models and solution methods were presented…

Effective features can improve the performance of a model, which can thus help us understand the characteristics and underlying structure of complex data. Previous feature selection methods usually cannot keep more local structure…

Learning to Optimize (L2O) approaches, including algorithm unrolling, plug-and-play methods, and hyperparameter learning, have garnered significant attention and have been successfully applied to the Alternating Direction Method of…

Nonnegative matrix factorization (NMF) often relies on the separability condition for tractable algorithm design. Separability-based NMF is mainly handled by two types of approaches, namely, greedy pursuit and convex programming. A notable…

This paper proposes a multiblock alternating direction method of multipliers for solving a class of multiblock nonsmooth nonconvex optimization problem with nonlinear coupling constraints. We employ a majorization minimization procedure in…

In this paper, we investigate a formula to solve systems of the form (B + {\sigma}I)x = y, where B is a limited-memory BFGS quasi-Newton matrix and {\sigma} is a positive constant. These types of systems arise naturally in large-scale…

When equipped with efficient optimization algorithms, the over-parameterized neural networks have demonstrated high level of performance even though the loss function is non-convex and non-smooth. While many works have been focusing on…

This study focuses on the feature extraction problem in multi-modal data regression. To address three core challenges in real-world scenarios: limited and non-IID data, effective extraction and fusion of multi-modal information, and…

This paper proposes a provably convergent multiblock ADMM for nonconvex optimization with nonlinear dynamics constraints, overcoming the divergence issue in classical extensions. We consider a class of optimization problems that arise from…

In this paper, we study nonconvex constrained stochastic zeroth-order optimization problems, for which we have access to exact information of constraints and noisy function values of the objective. We propose a Bregman linearized augmented…