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Sorting is a common and ubiquitous activity for computers. It is not surprising that there exist a plethora of sorting algorithms. For all the sorting algorithms, it is an accepted performance limit that sorting algorithms are linearithmic…
This paper offers a matrix-free first-order numerical method to solve large-scale conic optimization problems. Solving systems of linear equations pose the most computationally challenging part in both first-order and second-order numerical…
A moldable job is a job that can be executed on an arbitrary number of processors, and whose processing time depends on the number of processors allotted to it. A moldable job is monotone if its work doesn't decrease for an increasing…
We consider the classical scheduling problem on a single machine, on which we need to schedule sequentially $n$ given jobs. Every job $j$ has a processing time $p_j$ and a priority weight $w_j$, and for a given schedule a completion time…
Designing and implementing systems as an interconnection of smaller subsystems is a common practice for modularity and standardization of components and design algorithms. Although not typically cast in this framework, many of these…
As demonstrated in many areas of real-life applications, neural networks have the capability of dealing with high dimensional data. In the fields of optimal control and dynamical systems, the same capability was studied and verified in many…
In this work, we reveal a rich combinatorial structure underlying exact minimax optimal algorithms for classical nonexpansive fixed-point problems. This viewpoint unifies all extremal optimal methods and provides a systematic and practical…
This paper considers the distributed nonconvex optimization problem of minimizing a global cost function formed by a sum of local cost functions by using local information exchange. We first consider a distributed first-order primal-dual…
Nonnegative matrix factorization is the following problem: given a nonnegative input matrix $V$ and a factorization rank $K$, compute two nonnegative matrices, $W$ with $K$ columns and $H$ with $K$ rows, such that $WH$ approximates $V$ as…
Scheduling problems are fundamental in combinatorial optimization. Much work has been done on approximation algorithms for NP-hard cases, but relatively little is known about exact solutions when some part of the input is a fixed parameter.…
Fixed-parameter tractability analysis and scheduling are two core domains of combinatorial optimization which led to deep understanding of many important algorithmic questions. However, even though fixed-parameter algorithms are appealing…
An effective method for generating linear equations of maximal symmetry in their much general normal form is obtained. In the said normal form, the coefficients of the equation are differential functions of the coefficient of the term of…
We study the computability of the operator norm of a matrix with respect to norms induced by linear operators. Our findings reveal that this problem can be solved exactly in polynomial time in certain situations, and we discuss how it can…
In this paper, we study the assortment optimization problem under the mixed-logit customer choice model. While assortment optimization has been a major topic in revenue management for decades, the mixed-logit model is considered one of the…
We consider anti-unification for simply typed lambda terms in associative, commutative, and associative-commutative theories and develop a sound and complete algorithm which takes two lambda terms and computes their generalizations in the…
Linear algebraic expressions are the essence of many computationally intensive problems, including scientific simulations and machine learning applications. However, translating high-level formulations of these expressions to efficient…
We define the supermodular rank of a function on a lattice. This is the smallest number of terms needed to decompose it into a sum of supermodular functions. The supermodular summands are defined with respect to different partial orders. We…
We design optimal $2 \times N$ ($2 <N$) matrices, with unit columns, so that the maximum condition number of all the submatrices comprising 3 columns is minimized. The problem has two applications. When estimating a 2-dimensional signal by…
Let us assume that $f$ is a continuous function defined on the unit ball of $\mathbb R^d$, of the form $f(x) = g (A x)$, where $A$ is a $k \times d$ matrix and $g$ is a function of $k$ variables for $k \ll d$. We are given a budget $m \in…
Resolvent compositions were recently introduced as monotonicity-preserving operations that combine a set-valued monotone operator and a bounded linear operator. They generalize in particular the notion of a resolvent average. We analyze the…