Related papers: Tropical implementation of the Analytical Hierarch…
Finding a common factor of two multivariate polynomials with approximate coefficients is a problem in symbolic-numeric computing. Taking a tropical view on this problem leads to efficient preprocessing techniques, applying polyhedral…
Alternating minimization represents a widely applicable and empirically successful approach for finding low-rank matrices that best fit the given data. For example, for the problem of low-rank matrix completion, this method is believed to…
In this PhD thesis we propose an algorithmic approach to the study of the Hilbert scheme. Developing algorithmic methods, we also obtain general results about Hilbert schemes. In Chapter 1 we discuss the equations defining the Hilbert…
A class of algorithms for the solution of discrete material optimization problems in electromagnetic applications is discussed. The idea behind the algorithm is similar to that of the sequential programming. However, in each major iteration…
In this work, we show that for linearly constrained optimization problems the primal-dual hybrid gradient algorithm, analyzed by Chambolle and Pock [3], can be written as an entirely primal algorithm. This allows us to prove convergence of…
A very brief introduction to tropical and idempotent mathematics is presented. Tropical mathematics can be treated as a result of a dequantization of the traditional mathematics as the Planck constant tends to zero taking imaginary values.…
We propose NEP_MiniMax, a novel computational method for solving nonlinear eigenvalue problems (NEPs) $T(\lambda)\mathbf{u}= 0$ on compact continua $\Omega \subset \mathbb{C}$. The method combines two key components: (1) a rational minimax…
We propose an asymmetric affinity score for representing the complexity of utilizing the knowledge of one task for learning another one. Our method is based on the maximum bipartite matching algorithm and utilizes the Fisher Information…
Pairwise comparison methods, such as Fuzzy Preference Relations and Saaty's Multiplicative Preference Relations, are widely used to model expert judgments in multi-criteria decision-making. However, their application is limited by the high…
We introduce a novel approach to portfolio optimization that leverages hierarchical graph structures and the Schur complement method to systematically reduce computational complexity while preserving full covariance information. Inspired by…
Increasing spatial and temporal resolution of numerical models continues to propel progress in hydrological sciences, but, at the same time, it has strained the ability of modern automatic calibration methods to produce realistic model…
The tropical semiring is a semiring of extended real numbers, where the operations of `max' and `+' replace the usual addition and multiplication, respectively. Difference equations obtained from the ultradiscrete limit of discrete…
We propose a test of fairness in score-based ranking systems called matched pair calibration. Our approach constructs a set of matched item pairs with minimal confounding differences between subgroups before computing an appropriate measure…
One-sided linear systems of the form ``$Ax=b$'' are well-known and extensively studied over the tropical (max-plus) semiring and wide classes of related idempotent semirings. The usual approach is to first find the greatest solution to such…
We present a hierarchical computation approach for solving finite-time optimal control problems using operator splitting methods. The first split is performed over the time index and leads to as many subproblems as the length of the…
In this article a topology optimization method is developed, which is aware of material uncertainties. The uncertainties are handled in a worst-case sense, i.e. the worst possible material distribution over a given uncertainty set is taken…
In this paper, we investigate the computational complexity of the knapsack problem and subset sum problem for the following tropical algebraic structures. We consider the semigroup of square matrices of size $k \times k$ with non-negative…
In recent years, low-rank tensor completion (LRTC) has received considerable attention due to its applications in image/video inpainting, hyperspectral data recovery, etc. With different notions of tensor rank (e.g., CP, Tucker, tensor…
We consider the Adaptive Regularization with Cubics approach for solving nonconvex optimization problems and propose a new variant based on inexact Hessian information chosen dynamically. The theoretical analysis of the proposed procedure…
In this paper, we study linear programming based approaches to the maximum matching problem in the semi-streaming model. The semi-streaming model has gained attention as a model for processing massive graphs as the importance of such graphs…