Related papers: Pricing Filtering in Dantzig-Wolfe Decomposition
In data analysis, there continues to be a need for interpretable dimensionality reduction methods whereby instrinic meaning associated with the data is retained in the reduced space. Standard approaches such as Principal Component Analysis…
Random cost simulations were introduced as a method to investigate optimization problems in systems with conflicting constraints. Here I study the approach in connection with the training of a feed-forward multilayer perceptron, as used in…
This paper explores the use of Column Generation (CG) techniques in constructing univariate binary decision trees for classification tasks. We propose a novel Integer Linear Programming (ILP) formulation, based on root-to-leaf paths in…
This paper considers the problem of matrix completion when some number of the columns are completely and arbitrarily corrupted, potentially by a malicious adversary. It is well-known that standard algorithms for matrix completion can return…
We introduce a tree-based formulation for the minimum-cost multi-commodity flow problem that addresses large-scale instances. The method decomposes the source-based model by representing flows as convex combinations of trees rooted at…
Disruptions in the operational flow of rail traffic can lead to conflicts between train movements, such that a scheduled timetable can no longer be realised. This is where dispatching is applied, existing conflicts are resolved and a…
Two-phase methods are commonly used to solve bi-objective combinatorial optimization problems. In the first phase, all extreme supported nondominated points are generated through a dichotomic search. This phase also allows the…
Cut generation and lifting are key components for the performance of state-of-the-art mathematical programming solvers. This work proposes a new general cut-and-lift procedure that exploits the combinatorial structure of 0-1 problems via a…
We consider the problem of developing interpretable and computationally efficient matrix decomposition methods for matrices whose entries have bounded support. Such matrices are found in large-scale DNA methylation studies and many other…
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This paper explores the relationship between matrix factorizations and linear matrix equations. It shows that every matrix factorization defines two hidden projectors, one for the column space and one for the row space of a matrix, and how…
Estimating the diagonal entries of a matrix, that is not directly accessible but only available as a linear operator in the form of a computer routine, is a common necessity in many computational applications, especially in image…
We propose a novel decomposition framework for the distributed optimization of general nonconvex sum-utility functions arising naturally in the system design of wireless multiuser interfering systems. Our main contributions are: i) the…
Submodular functions are an important class of functions in combinatorial optimization which satisfy the natural properties of decreasing marginal costs. The study of these functions has led to strong structural properties with applications…
We consider the problem of matrix column subset selection, which selects a subset of columns from an input matrix such that the input can be well approximated by the span of the selected columns. Column subset selection has been applied to…
Interpretability of Deep Neural Networks has become a major area of exploration. Although these networks have achieved state of the art accuracy in many tasks, it is extremely difficult to interpret and explain their decisions. In this work…
We study the problem of computing the matrix exponential of a block triangular matrix in a peculiar way: Block column by block column, from left to right. The need for such an evaluation scheme arises naturally in the context of option…
With the abundance of available data, many enterprises seek to implement data-driven prescriptive analytics to help them make informed decisions. These prescriptive policies need to satisfy operational constraints, and proactively eliminate…
The optimal pricing problem is a fundamental problem that arises in combinatorial auctions. Suppose that there is one seller who has indivisible items and multiple buyers who want to purchase a combination of the items. The seller wants to…
We propose a very simple preconditioning method for integer programming feasibility problems: replacing the problem b' <= Ax <= b, x \in Z^n with b' <= AUy <= b, y \in Z^n, where U is a unimodular matrix computed via basis reduction, to…