Related papers: Uniform and Monotone Line Sum Optimization
We investigate the question whether Subset Sum can be solved by a polynomial-time algorithm with access to a certificate of length poly(k) where k is the maximal number of bits in an input number. In other words, can it be solved using only…
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…
This paper introduces a novel algorithmic solution for the approximation of a given multivariate function by a nomographic function that is composed of a one-dimensional continuous and monotone outer function and a sum of univariate…
Numerous interesting properties in nonlinear systems analysis can be written as polynomial optimization problems with nonconvex sum-of-squares problems. To solve those problems efficiently, we propose a sequential approach of local…
Let $\mathscr{A}$ be a nonempty set of infinite matrices of linear operators between two topological vector spaces. We show that a sequence is uniformly $\mathscr{A}$-summable if and only if it is $B$-summable for all matrices $B$ of linear…
We study an optimization problem in which the objective is given as a sum of logarithmic-polynomial functions. This formulation is motivated by statistical estimation principles such as maximum likelihood estimation, and by loss functions…
A common theme in mathematics is to define generalized solutions to deal with problems that potentially do not have solutions. A classical example is the introduction of least squares solutions via the normal equations associated with a…
A homotopy method for multi-objective optimization that produces uniformly sampled Pareto fronts by construction is presented. While the algorithm is general, of particular interest is application to simulation-based engineering…
New iterative methods for solving linear equations are presented that are easy to use, generalize good existing methods, and appear to be faster. The new algorithms mix two kinds of linear recurrence formulas. Older methods have either high…
In this survey we consider polynomial optimization problems, asking to minimize a polynomial function over a compact semialgebraic set, defined by polynomial inequalities. This models a great variety of (in general, nonlinear nonconvex)…
Submodular function optimization has numerous applications in machine learning and data analysis, including data summarization which aims to identify a concise and diverse set of data points from a large dataset. It is important to…
Linear vector equations and inequalities are considered defined in terms of idempotent mathematics. To solve the equations, we apply an approach that is based on the analysis of distances between vectors in idempotent vector spaces. The…
The intention of this note is two-fold. First, we study integer optimization problems in standard form defined by $A \in\mathbb{Z}^{m\times{}n}$ and present an algorithm to solve such problems in polynomial-time provided that both the…
We study the best approximation problem: \[ \displaystyle \min_{\alpha\in \mathbb R^m}\max_{1\leq i\leq n}\left|y_i -\sum_{j=1}^m \alpha_j \Gamma_j ({\bf x}_i) \right|. \] Here: $\Gamma:=\left\{\Gamma_1,...,\Gamma_m\right\}$ is a list of…
Linear programming is a powerful method in combinatorial optimization with many applications in theory and practice. For solving a linear program quickly it is desirable to have a formulation of small size for the given problem. A useful…
The goal of this paper is to present an overview of the software collection for the solution of linear and nonlinear semidefinite optimization problems PENNON. In the first part we present theoretical and practical details of the underlying…
This paper connects discrete optimal transport to a certain class of multi-objective optimization problems. In both settings, the decision variables can be organized into a matrix. In the multi-objective problem, the notion of Pareto…
In this work, we study the problem of monotone non-submodular maximization with partition matroid constraint. Although a generalization of this problem has been studied in literature, our work focuses on leveraging properties of partition…
The row (column) completion problem of polynomial matrices of given degree with prescribed eigenstructure has been studied in \cite{AmBaMaRo23}, where several results of prescription of some of the four types of invariants that form the…
The study of combinatorial optimization problems with a submodular objective has attracted much attention in recent years. Such problems are important in both theory and practice because their objective functions are very general. Obtaining…