Related papers: Combining Penalty-based and Gauss-Seidel Methods f…

In sparse Bayesian learning (SBL), Gaussian scale mixtures (GSMs) have been used to model sparsity-inducing priors that realize a class of concave penalty functions for the regression task in real-valued signal models. Motivated by the…

This paper studies generalized semi-infinite programs (GSIPs) defined with polyhedral parameter sets. Assume these GSIPs are given by polynomials. We propose a new approach to solve them as a disjunctive program. This approach is based on…

The Partial Information Decomposition (PID) [arXiv:1004.2515] provides a theoretical framework to characterize and quantify the structure of multivariate information sharing. A new method (Idep) has recently been proposed for computing a…

The primary goal of this paper is to provide an efficient solution algorithm based on the augmented Lagrangian framework for optimization problems with a stochastic objective function and deterministic constraints. Our main contribution is…

The shortest path network interdiction (SPNI) problem poses significant computational challenges due to its NP-hardness. Current solutions, primarily based on integer programming methods, are inefficient for large-scale instances. In this…

Process Planning and Scheduling (PPS) is an essential and practical topic but a very intractable problem in manufacturing systems. Many research use iterative methods to solve such problems; however, they cannot achieve satisfactory results…

We consider the problem of estimating the parameters of a Gaussian or binary distribution in such a way that the resulting undirected graphical model is sparse. Our approach is to solve a maximum likelihood problem with an added l_1-norm…

Some variants of the (block) Gauss--Seidel iteration for the solution of linear systems with $M$-matrices in (block) Hessenberg form are discussed. Comparison results for the asymptotic convergence rate of some regular splittings are…

Multigrid methods are well suited to large massively parallel computer architectures because they are mathematically optimal and display excellent parallelization properties. Since current architecture trends are favoring regular compute…

In this paper, we introduce a new stochastic approximation (SA) type algorithm, namely the randomized stochastic gradient (RSG) method, for solving an important class of nonlinear (possibly nonconvex) stochastic programming (SP) problems.…

In this work, we investigate a stochastic gradient descent method for solving inverse problems that can be written as systems of linear or nonlinear ill-posed equations in Banach spaces. The method uses only a randomly selected equation at…

In this work, we propose a Bayesian type sparse deep learning algorithm. The algorithm utilizes a set of spike-and-slab priors for the parameters in the deep neural network. The hierarchical Bayesian mixture will be trained using an…

Augmented Lagrangian dual augments the classical Lagrangian dual with a non-negative non-linear penalty function of the violation of the relaxed/dualized constraints in order to reduce the duality gap. We investigate the cases in which…

We consider the minimization of a sum of a smooth function with a nonsmooth composite function, where the composition is applied on a random linear mapping. This random composite model encompasses many problems, and can especially capture…

We propose a new exact approach for solving integer linear programming (ILP) problems which we will call projective splitting algorithms (PSAs). Unlike classical methods for solving ILP problems, PSAs conduct the search for the optimal…

For minimizing a strongly convex objective function subject to linear inequality constraints, we consider a penalty approach that allows one to utilize stochastic methods for problems with a large number of constraints and/or objective…

We propose a new approach to mixed-frequency regressions in a high-dimensional environment that resorts to Group Lasso penalization and Bayesian techniques for estimation and inference. In particular, to improve the prediction properties of…

In this paper, we consider a class of optimization problems constrained to the generalized Stiefel manifold. Such problems are fundamental to a wide range of real-world applications, including generalized canonical correlation analysis,…

Bayesian optimization relies on iteratively constructing and optimizing an acquisition function. The latter turns out to be a challenging, non-convex optimization problem itself. Despite the relative importance of this step, most algorithms…

Nonconvex and structured optimization problems arise in many engineering applications that demand scalable and distributed solution methods. The study of the convergence properties of these methods is in general difficult due to the…