Related papers: Column basis reduction, and decomposable knapsack …

We present a Julia package, DisjunctiveProgramming.jl, that extends the functionality in JuMP.jl to allow modeling problems via logical propositions and disjunctive constraints. Such models can then be reformulated into Mixed-Integer…

We consider a variant of the knapsack problem, where items are available with different possible weights. Using a separate budget for these item improvements, the question is: Which items should be improved to which degree such that the…

The bin packing problem exists widely in real logistic scenarios (e.g., packing pipeline, express delivery), with its goal to improve the packing efficiency and reduce the transportation cost. In this NP-hard combinatorial optimization…

Many statistical problems involve the estimation of a $\left(d\times d\right)$ orthogonal matrix $\textbf{Q}$. Such an estimation is often challenging due to the orthonormality constraints on $\textbf{Q}$. To cope with this problem, we…

In this paper, we consider the challenge of reconstructing jointly sparse vectors from linear measurements. Firstly, we show that by utilizing the rank of the output data matrix we can reduce the problem to a full column rank case. This…

Column generation is an iterative method used to solve a variety of optimization problems. It decomposes the problem into two parts: a master problem, and one or more pricing problems (PP). The total computing time taken by the method is…

In this paper we propose a product space reformulation to transform monotone inclusions described by finitely many operators on a Hilbert space into equivalent two-operator problems. Our approach relies on Pierra's classical reformulation…

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…

Many nonlinear optimal control and optimization problems involve constraints that combine continuous dynamics with discrete logic conditions. Standard approaches typically rely on mixed-integer programming, which introduces scalability…

The multiple knapsack problem (MKP) generalizes the classical knapsack problem by assigning items to multiple knapsacks subject to capacity constraints. It is used to model many real-world resource allocation and scheduling problems. In…

Radio-frequency portion of the electromagnetic spectrum is a scarce resource. Cognitive radio technology has emerged as a promising solution to overcome the spectrum scarcity bottleneck. Through this technology, secondary users (SUs) sense…

We study the $K$-item knapsack problem (i.e., $1.5$-dimensional KP), which is a generalization of the famous 0-1 knapsack problem (i.e., $1$-dimensional KP) in which an upper bound $K$ is imposed on the number of items selected. This…

Numerous applications require algorithms that can align partially overlapping point sets while maintaining invariance to geometric transformations (e.g., similarity, affine, rigid). This paper introduces a novel global optimization method…

We present a new algorithm for computing a truncated Markov basis of a lattice. In general, this new algorithm is faster than existing methods. We then extend this new algorithm so that it solves the linear integer feasibility problem with…

The present paper deals with the discrete inverse problem of reconstructing binary matrices from their row and column sums under additional constraints on the number and pattern of entries in specified minors. While the classical…

A general, {\em rectangular} kernel matrix may be defined as $K_{ij} = \kappa(x_i,y_j)$ where $\kappa(x,y)$ is a kernel function and where $X=\{x_i\}_{i=1}^m$ and $Y=\{y_i\}_{i=1}^n$ are two sets of points. In this paper, we seek a low-rank…

We consider supervised learning problems within the positive-definite kernel framework, such as kernel ridge regression, kernel logistic regression or the support vector machine. With kernels leading to infinite-dimensional feature spaces,…

We review some important ideas in the design and analysis of robust overlapping domain decomposition algorithms for high-contrast multiscale problems and propose a domain decomposition method better performance in terms of the number of…

Robust principal component analysis (RPCA) is a widely used tool for dimension reduction. In this work, we propose a novel non-convex algorithm, coined Iterated Robust CUR (IRCUR), for solving RPCA problems, which dramatically improves the…

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…