Related papers: Benders decomposition for the large-scale probabil…
Semidefinite programming (SDP) is a powerful framework from convex optimization that has striking potential for data science applications. This paper develops a provably correct randomized algorithm for solving large, weakly constrained SDP…
Motivated by the philosophy and phenomenal success of compressed sensing, the problem of reconstructing a matrix from a sampling of its entries has attracted much attention recently. Such a problem can be viewed as an information-theoretic…
Hybrid model predictive control with both continuous and discrete variables is widely applicable to robotic control tasks, especially those involving contact with the environment. Due to the combinatorial complexity, the solving speed of…
This paper considers the problems of unconstrained minimization of large scale smooth convex functions having block-coordinate-wise Lipschitz continuous gradients. The block coordinate descent (BCD) method are among the first optimization…
This paper presents a new hybrid classical-quantum approach to solve Mixed Integer Linear Programming (MILP) using neutral atom quantum computations. We apply Benders decomposition (BD) to segment MILPs into a master problem (MP) and a…
Sparse PCA (SPCA) is a fundamental model in machine learning and data analytics, which has witnessed a variety of application areas such as finance, manufacturing, biology, healthcare. To select a prespecified-size principal submatrix from…
In today's information systems, the availability of massive amounts of data necessitates the development of fast and accurate algorithms to summarize these data and represent them in a succinct format. One crucial problem in big data…
Conformal prediction (CP) is a framework to quantify uncertainty of machine learning classifiers including deep neural networks. Given a testing example and a trained classifier, CP produces a prediction set of candidate labels with a…
We consider the least squares regression problem, penalized with a combination of the $\ell_{0}$ and squared $\ell_{2}$ penalty functions (a.k.a. $\ell_0 \ell_2$ regularization). Recent work shows that the resulting estimators are of key…
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…
Leveraging the current generation of quantum devices to solve optimization problems of practical interest necessitates the development of hybrid quantum-classical (HQC) solution approaches. In this paper, a multi-cut Benders decomposition…
An effective technique for solving optimization problems over massive data sets is to partition the data into smaller pieces, solve the problem on each piece and compute a representative solution from it, and finally obtain a solution…
Many probabilistic inference tasks involve summations over exponentially large sets. Recently, it has been shown that these problems can be reduced to solving a polynomial number of MAP inference queries for a model augmented with randomly…
In the post-Moore era, the need for efficient solutions to non-deterministic polynomial-time (NP) problems is becoming more pressing. In this context, the Ising model implemented by the probabilistic computing systems with probabilistic…
Linear Programming (LP) is an important decoding technique for binary linear codes. However, the advantages of LP decoding, such as low error floor and strong theoretical guarantee, etc., come at the cost of high computational complexity…
Many annotation problems in computer vision can be phrased as integer linear programs (ILPs). The use of standard industrial solvers does not to exploit the underlying structure of such problems eg, the skeleton in pose estimation. The…
This paper proposes a joint decomposition method that combines La- grangian decomposition and generalized Benders decomposition, to efficiently solve multiscenario nonconvex mixed-integer nonlinear programming (MINLP) problems to global…
In this paper, we consider the optimization problem Submodular Cover (SCP), which is to find a minimum cardinality subset of a finite universe $U$ such that the value of a submodular function $f$ is above an input threshold $\tau$. In…
Configuration Optimization Problems (COPs), which involve minimizing a loss function over a set of discrete points $\boldsymbol{\gamma} \subset P$, are common in areas like Model Order Reduction, Active Learning, and Optimal Experimental…
We develop a decomposition algorithm for distributionally-robust two-stage stochastic mixed-integer convex cone programs, and its important special case of distributionally-robust two-stage stochastic mixed-integer second order cone…