相关论文: Combining Penalty-based and Gauss-Seidel Methods f…

In this paper, we propose a unified primal-dual algorithm framework based on the augmented Lagrangian function for composite convex problems with conic inequality constraints. The new framework is highly versatile. First, it not only covers…

Multistage stochastic programs can be approximated by restricting policies to follow decision rules. Directly applying this idea to problems with integer decisions is difficult because of the need for decision rules that lead to integral…

Many contemporary signal processing, machine learning and wireless communication applications can be formulated as nonconvex nonsmooth optimization problems. Often there is a lack of efficient algorithms for these problems, especially when…

The Stackelberg prediction game (SPG) has been extensively used to model the interactions between the learner and data provider in the training process of various machine learning algorithms. Particularly, SPGs played prominent roles in…

For a symmetric positive semidefinite linear system of equations $\mathcal{Q} {\bf x} = {\bf b}$, where ${\bf x} = (x_1,\ldots,x_s)$ is partitioned into $s$ blocks, with $s \geq 2$, we show that each cycle of the classical block symmetric…

Multi-physics models governed by coupled partial differential equation (PDE) systems, are naturally suited for partitioned, or modular numerical solution strategies. Although widely used in tackling deterministic coupled models, several…

Due to the intricate of real-world road topologies and the inherent complexity of autonomous vehicles, cooperative decision-making for multiple connected autonomous vehicles (CAVs) remains a significant challenge. Currently, most methods…

We propose a hierarchical architecture for efficiently computing high-quality solutions to structured mixed-integer programs (MIPs). To reduce computational effort, our approach decouples the original problem into a higher level problem and…

We propose a semi-proximal augmented Lagrangian based decomposition method for convex composite quadratic conic programming problems with primal block angular structures. Using our algorithmic framework, we are able to naturally derive…

One of the challenges encountered in optimization of mechanical structures, in particular in what is known as topology optimization, is the size of the problems, which can easily involve millions of variables. A basic example is the minimum…

The Set Cover Problem (SCP) and the Hitting Set Problem (HSP) are well-studied optimization problems. In this paper we introduce the Reward-Penalty-Selection Problem (RPSP) which can be understood as a combination of the SCP and the HSP…

For many mixed-integer programming (MIP) problems, high-quality dual bounds can be obtained either through advanced formulation techniques coupled with a state-of-the-art MIP solver, or through semidefinite programming (SDP) relaxation…

In this paper, we investigate combining blocking and collapsing -- two widely used strategies for improving the accuracy of Gibbs sampling -- in the context of probabilistic graphical models (PGMs). We show that combining them is not…

This paper surveys the trend of leveraging machine learning to solve mixed integer programming (MIP) problems. Theoretically, MIP is an NP-hard problem, and most of the combinatorial optimization (CO) problems can be formulated as the MIP.…

This paper considers stochastic optimization problems with weakly convex objective and constraint functions. We propose Prox-PEP, a proximal method equipped with quadratic subproblems. To handle nonlinear equality constraints, we employ an…

We consider the problem of learning a sparse graph underlying an undirected Gaussian graphical model, a key problem in statistical machine learning. Given $n$ samples from a multivariate Gaussian distribution with $p$ variables, the goal is…

This paper is concerned with a novel deep learning method for variational problems with essential boundary conditions. To this end, we first reformulate the original problem into a minimax problem corresponding to a feasible augmented…

We present new convergence estimates for the iterated penalty method applied to structure-preserving discretizations of linear generalized saddle point systems. The method may be viewed as an Uzawa iteration on an augmented Lagrangian…

We propose a multi-criteria Composite Index Method (CIM) to compare the performance of alternative approaches to solving an optimization problem. The CIM is convenient in those situations when neither approach dominates the other when…

We consider a discrete optimization formulation for learning sparse classifiers, where the outcome depends upon a linear combination of a small subset of features. Recent work has shown that mixed integer programming (MIP) can be used to…